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I want to find literature that asserts that employee performance does not follow a Gaussian distribution and may follow alternative distributions like the Pareto distribution. I am interested in theoretical discussions, empirical studies, literature reviews, and original research articles, especially within economics, management, and psychology journals. If available, I'm also interested in studies that explore the connection between these performance distributions and employee salary distributions.

Report

Research extensively supports that employee performance does not follow a Gaussian distribution and often follows alternative distributions like the Pareto distribution, with significant implications for performance appraisal and compensation strategies [1, 2, 3, 8].

Details:

Pareto Distribution in Employee Performance:
- O'Boyle and Aguinis (2012) conducted a robust empirical investigation across five studies with 198 samples (632,599 individuals). They found that individual performance follows a Paretian (power law) distribution rather than a normal distribution, impacting performance appraisal and human resource practices [1].
- Aguinis and O’Boyle (2014) further discuss the concept of 'star performers' and how a power law distribution of performance challenges traditional HR practices. They propose implications for compensation, suggesting that high performers justify significantly higher rewards due to their outsized contributions [2].
- Aguinis et al. (2016) analyze the conditions under which individual productivity follows nonnormal heavy-tailed distributions, emphasizing the significant role of cumulative advantage in producing star performers [3].

Empirical and Theoretical Underpinnings:
- Bradley and Aguinis (2022) compiled and analyzed 274 team performance distributions, finding that only 11% were normally distributed. They identified the power law with an exponential cutoff as the most common distribution, providing further evidence against the Gaussian assumption in team contexts [4].
- Grubb (1985) showed that the earnings of the top 10-20% of individuals follow a Pareto distribution, emphasizing that those in senior management roles have a disproportionate impact on company output and consequently earn much higher salaries [5].
- Andriani and McKelvey (2009) provided a theoretical basis for the prevalence of power laws in organizational dynamics, advocating for a shift in research and practical approaches to accommodate these findings [8].
Connection to Salary Distributions:
- Harrison (1981) re-examined earnings data and confirmed that while the bulk of earnings are lognormal, the upper tail follows a Pareto distribution, hinting at the impact of rare but extremely high performers [7].
- Clementi and Giammatteo (2010) found that Italian labor income distributions exhibit a Pareto-like right-skewed pattern, particularly among self-employed individuals and non-standard employment [15].
- Geerolf (2016) demonstrated how Pareto distributions arise in labor earnings by modeling static assignment with complementarities in production, tying it to heterogeneous performance outcomes [19].
Methodological Considerations and Critiques:
- Spain et al. (2013) questioned the conclusion that job performance follows a power law, emphasizing the need for rigorous statistical testing against comparable alternatives [12].
- Beck et al. (2013) posited that extreme nonnormal results could be attributed to certain measurement characteristics, urging a careful consideration of performance metrics [20].

Conclusions: The existing literature strongly supports the assertion that employee performance often follows a Pareto or other non-Gaussian distributions rather than a normal distribution. This shift in understanding necessitates a reconsideration of various management practices, including performance evaluations, personnel selection, and compensation strategies. The connection between performance distributions and earnings is particularly evident in the upper tail, where a small number of high performers receive disproportionately high rewards, aligning with Pareto's principles.

References

Last 5 years

Last 2 years

> 1 citation per year

> 5 citations per year

Topic Match

Cit./Year

Year

Paper

Paper Relevance Summary

99.8%

18.3

2012

[1] THE BEST AND THE REST: REVISITING THE NORM OF NORMALITY OF INDIVIDUAL PERFORMANCE Ernest H. O’Boyle and Herman Aguinis https://doi.org/10.5465/AMBPP.2011.65869128 2012 - 235 citations - Show abstract - Cite 99.8% topic match

Shows that individual performance follows a Paretian distribution. Conducted studies across 198 samples, finding performance does not fit a Gaussian distribution. Implications for performance appraisal, personnel selection, leadership, and motivation practices are discussed.

99.5%

20.8

2014

[2] Star Performers in Twenty‐First Century Organizations Herman Aguinis and Ernest H. O’Boyle Personnel Psychology 2014 - 220 citations - Show abstract - Cite 99.5% topic match

Asserts performance follows a power law distribution rather than Gaussian. Describes the emergence of star performers contributing disproportionate output. Discusses implications for management practices including compensation, highlighting its relevance to salary distributions.

99.4%

7.1

2016

[3] CUMULATIVE ADVANTAGE: CONDUCTORS AND INSULATORS OF HEAVY-TAILED PRODUCTIVITY DISTRIBUTIONS AND PRODUCTIVITY STARS Herman Aguinis, ..., and Harry Joo Personnel Psychology 2016 - 63 citations - Show abstract - Cite 99.4% topic match

Examines heavy-tailed productivity distributions among individuals. Discusses how and why productivity may follow nonnormal distributions like the Pareto distribution. Explores implications for HR systems, including compensation and training strategies, in organizations.

99.4%

4.4

2022

[4] Team Performance: Nature and Antecedents of Nonnormal Distributions Kyle J. Bradley and Herman Aguinis Organization Science 2022 - 10 citations - Show abstract - Cite Abstract: Team research typically assumes that team performance is normally distributed: teams cluster around average performance, performance variability is not substantial, and few teams inhabit the upper range of the distribution. Ironically, although most team research and methodological practices rely on the normality assumption, many theories actually imply nonnormality (e.g., performance spirals, team composition, team learning, punctuated equilibrium). Accordingly, we investigated the nature and antecedents of team performance distributions by relying on 274 performance distributions including 200,825 teams (e.g., sports, politics, firefighters, information technology, customer service) and more than 500,000 workers. First, regarding their overall nature, only 11% of the distributions were normal, star teams are much more prevalent than predicted by normality, the power law with an exponential cutoff is the most dominant distribution among nonnormal distributions (i.e., 73%), and incremental differentiation (i.e., differential performance trajectories across teams) is the best explanation for the emergence of these distributions. Second, this conclusion remained unchanged after examining theory-based boundary conditions (i.e., tournament versus nontournament contexts, performance as aggregation of individual-level performance versus performance as a team-level construct, performance assessed with versus without a hard left-tail zero, and more versus less sample homogeneity). Third, we used the team learning curve literature as a conceptual framework to test hypotheses and found that authority differentiation and lower temporal stability are associated with distributions with larger performance variability (i.e., a greater proportion of star teams). We discuss implications for existing theory, future research directions, and methodological practices (e.g., need to check for nonnormality, Bayesian analysis, outlier management). 99.4% topic match

Shows team performance does not follow a normal distribution. Analyzes 274 distributions, finding power law with an exponential cutoff prevalent. Includes diverse fields; confirms findings across various team contexts and conditions.

99.3%

0.2

1985

[5] ABILITY AND POWER OVER PRODUCTION IN THE DISTRIBUTION OF EARNINGS David B Grubb The Review of Economics and Statistics 1985 - 9 citations - Show abstract - Cite 99.3% topic match

Provides empirical evidence of a Pareto-like earnings distribution in top earners. Shows top 10-20% of earners follow a Pareto form, linked to job performance impact. Explains high earnings via profit-maximizing behavior and competitive bidding for top management, relevant to the link between performance and salary distributions.

99.3%

0.7

2012

[6] Disobeying Power Laws: Perils for Theory and Method G. Crawford Econometric Modeling: Theoretical Issues in Microeconometrics eJournal 2012 - 9 citations - Show abstract - Cite - PDF 99.3% topic match

Shows that organizational inputs and outcomes are power-law (Pareto) distributed. Contrasts with the myth of normal (Gaussian) distribution, highlighting the unstable means and disproportionate influence of extreme outcomes. Emphasizes the need for research designs that assume interdependence and nonlinear relationships, which could impact performance and compensation structures.

99.1%

1.4

1981

[7] Earnings by Size: A Tale of Two Distributions A. Harrison The Review of Economic Studies 1981 - 59 citations - Show abstract - Cite - PDF 99.1% topic match

Re-examines the distribution of earnings using Pareto and lognormal functions. Uses British New Earnings Survey data disaggregated by occupational groups to compare these distributions. Considers goodness of fit and provides detailed parameter estimates, particularly assessing the superiority of Pareto in the upper tail.

97.9%

12.5

2009

[8] From Gaussian to Paretian Thinking: Causes and Implications of Power Laws in Organizations P. Andriani and B. McKelvey Journal Not Provided 2009 - 200 citations - Show abstract - Cite 97.9% topic match

Provides evidence of power laws over Gaussian distributions in organizational contexts. Highlights the prevalence of Pareto rank/frequency distributions and their implications for organizational research and management. Discusses 15 scale-free theories relevant to organizational dynamics, emphasizing the importance of extremes over averages.

97.1%

2.1

2016

[9] USING A COMPUTATIONAL MODEL TO UNDERSTAND POSSIBLE SOURCES OF SKEWS IN DISTRIBUTIONS OF JOB PERFORMANCE J. Vancouver, ..., and Justin Purl Personnel Psychology 2016 - 17 citations - Show abstract - Cite 97.1% topic match

Shows sources of skewed performance distributions using computational modeling. Identifies factors like luck, multiplicative dynamics, and Matthew effects leading to positively skewed performance distributions. Relevant to understanding non-Gaussian distributions but does not focus specifically on the Pareto distribution or connect to salary distributions.

95.1%

4.5

2017

[10] Not All Nonnormal Distributions Are Created Equal: Improved Theoretical and Measurement Precision Harry Joo, ..., and Kyle J. Bradley Journal of Applied Psychology 2017 - 35 citations - Show abstract - Cite 95.1% topic match

Introduces a taxonomy of individual output distributions. Implements a method to compare distributions using empirical data from various occupations. Finds that 75% of samples fit exponential tail distributions over Gaussian, potentially challenging existing beliefs about performance metrics.

94.7%

0.0

2012

[11] PerILs FOr THeOry anD MeTHOD G. Opher Journal Not Provided 2012 - 0 citations - Show abstract - Cite 94.7% topic match

The paper argues against the assumption of Gaussian distributions in organizational contexts. It highlights that inputs and outcomes in organizations follow power-law distributions (Pareto), not normal distributions. Emphasizes how adopting research methods that acknowledge non-Gaussian distributions can yield more accurate theories and practical insights.

94.4%

0.0

2013

[12] Is Individual Job Performance Distributed According to a Power Law? A Review of Methods for Comparing Heavy-Tailed Distributions Seth M. Spain, ..., and Bradley J. Brummel https://doi.org/10.2139/SSRN.2238126 2013 - 0 citations - Show abstract - Cite 94.4% topic match

Challenges the assertion that job performance follows a power law. Compares normal, log-normal, and Pareto distributions using statistically principled testing methods. Discusses the necessity of comparing power-law models to plausible alternatives, and reviews methods for non-normal distributions.

92.6%

0.1

2017

[13] Stars and Skews Rise and Fall: A Mathematical Multilevel Adventure Avi I Turetsky https://doi.org/10.5465/AMBPP.2017.10158ABSTRACT 2017 - 1 citations - Show abstract - Cite 92.6% topic match

Provides insights on star performers and skewed performance distributions. Explores the impact of skewed performance distributions on organizational strategies and behaviors. May discuss theoretical and empirical findings relevant to non-Gaussian distributions, especially in management contexts.

91.3%

0.3

2012

[14] Emerging Scalability and Extreme Outcomes in New Ventures: Power-Law Analyses of Three Studies G. Crawford https://doi.org/10.5465/AMBPP.2012.305 2012 - 4 citations - Show abstract - Cite 91.3% topic match

Shows that performance-based outcomes follow a non-Gaussian, power-law distribution. Analyzes three studies revealing extreme outcomes and scalability in new ventures. Relevant to understanding performance distribution but focused on entrepreneurship, not explicitly on employee salary distributions.

91.3%

0.0

2010

[15] The Pareto Law and the Distribution of Labour Income in Italy F. Clementi and M. Giammatteo European Economics: Labor & Social Conditions eJournal 2010 - 0 citations - Show abstract - Cite - PDF 91.3% topic match

Provides empirical examination of labour earnings distribution in Italy. Shows a Pareto-type distribution for earnings, with a right-skewed, long right tail. Highlights the impact of self-employment and non-standard employment in shaping income inequality.

91.1%

0.1

1970

[16] Statistical theories of success. C. Zener Proceedings of the National Academy of Sciences of the United States of America 1970 - 6 citations - Show abstract - Cite - PDF 91.1% topic match

Shows that the Pareto distribution models high success rates well. Compares Pareto and log-normal distributions against publishing success, noting Pareto fits tail (high success, income) distributions. Indicates relevance by linking Pareto distribution with performance and income, supporting non-Gaussian performance distribution discussions.

90.3%

0.4

2022

[17] The Dynamics Underlying the Rise of Star Performers. L. R. Zwerwer and R. D. Den Hartigh Nonlinear dynamics, psychology, and life sciences 2022 - 1 citations - Show abstract - Cite 90.3% topic match

Provides insights into the dynamics of star performers. Explores multi-dimensional processes and parameters influencing tail-heaviness of performance distributions. Relevant for understanding distributive properties and dynamics behind heavy-tailed performance distributions, although not specific to Pareto distribution or salary link.

89.9%

0.0

2020

[18] A Simple Theory of Pareto Earnings Harmenberg Journal Not Provided 2020 - 0 citations - Show abstract - Cite 89.9% topic match

Provides a model generating a Pareto distribution in earnings. Shows earnings are determined by niche-specific labor supply and demand constraints. Relates earnings distribution to worker distribution across niches, highlighting extreme-value theory applicability.

88.3%

3.7

2016

[19] A Theory of Pareto Distributions F. Geerolf Journal Not Provided 2016 - 33 citations - Show abstract - Cite 88.3% topic match

Shows that Pareto distributions arise from production functions in static assignment models. Demonstrates Pareto distributions for CEO and manager control span using French employer-employee data. Explains firm size and labor income heterogeneity but does not directly address employee performance distribution.

85.3%

4.0

2013

[20] On the Distribution of Job Performance: The Role of Measurement Characteristics in Observed Departures from Normality James W. Beck, ..., and P. Sackett Personnel Psychology 2013 - 44 citations - Show abstract - Cite 85.3% topic match

Challenges the non-Gaussian job performance assertion by O'Boyle and Aguinis. Attributes observed nonnormal performance to measurement criteria not considered by O'Boyle and Aguinis. Relevant for understanding performance measure characteristics but does not directly support Pareto distribution or salary link.

83.3%

0.3

2004

[21] On Pareto’s law and the determinants of Pareto exponents W. Reed Journal of Income Distribution® 2004 - 7 citations - Show abstract - Cite 83.3% topic match

Effectively relates individual income growth to Pareto distribution characteristics. Explains Paretian behavior in income distributions using a stochastic model based on Gibrat's law and workforce growth rates. Focuses on income distribution rather than directly addressing employee performance or salary distribution connections.

81.8%

0.3

2013

[22] Star Performers in Twenty-First-Century Organizations Herman Aguinis and Ernest H. O’Boyle https://doi.org/10.5465/AMBPP.2013.35 2013 - 3 citations - Show abstract - Cite 81.8% topic match

78.1%

2.3

2017

[23] Skew and heavy‐tail effects on firm performance Shige Makino and C. M. Chan Southern Medical Journal 2017 - 17 citations - Show abstract - Cite 78.1% topic match

77.3%

1.6

2019

[24] Pareto Models for Top Incomes Arthur Charpentier and Emmanuel Flachaire Journal Not Provided 2019 - 9 citations - Show abstract - Cite 77.3% topic match

76.6%

0.3

2011

[25] Using Power-Law Science to Enhance Knowledge for Practical Relevance Hind Benbya and B. McKelvey https://doi.org/10.5465/AMBPP.2011.65870517 2011 - 4 citations - Show abstract - Cite 76.6% topic match

66.2%

0.5

2012

[26] STRATEGIC IMPLICATIONS OF POWER-LAW DISTRIBUTIONS IN THE CREATION AND EMERGENCE OF NEW VENTURES: POWER-LAW ANALYSES IN THREE PANEL STUDIES G. Crawford and B. McKelvey Frontiers of entrepreneurship research 2012 - 7 citations - Show abstract - Cite 66.2% topic match

Shows entrepreneurial outcomes follow a power-law distribution. Examines high-growth firms using power-law analyses across multiple datasets. Uses complexity science perspective, may inform about disproportionate impact of top performers.

64.5%

0.7

2014

[27] Tournaments and Superstar Models: A Mixture of Two Pareto Distributions Abdoul Aziz Junior Ndoye and M. Lubrano https://doi.org/10.1108/S1049-258520140000022015 2014 - 7 citations - Show abstract - Cite 64.5% topic match

63.9%

0.0

1970

[28] Statistical Theories ofSuccess C. Zener Journal Not Provided 1970 - 0 citations - Show abstract - Cite 63.9% topic match

61.7%

1.3

2017

[29] On the Distribution of Worker Productivity: The Case of Teacher Effectiveness and Student Achievement Dan Goldhaber and R. Startz Statistics and Public Policy 2017 - 10 citations - Show abstract - Cite 61.7% topic match

61.5%

0.0

2009

[30] Research Performance and Resource Allocation D. Hicks and Sylvan Katz Journal Not Provided 2009 - 0 citations - Show abstract - Cite 61.5% topic match

50.4%

0.2

2011

[31] Using scale-free processes to explain punctuated-change in management-relevant phenomena P. Andriani and B. McKelvey https://doi.org/10.1504/IJCLM.2011.042547 2011 - 3 citations - Show abstract - Cite 50.4% topic match

49.8%

0.0

2021

[32] RUNNING HEAD: DISTRIBUTION NEGLECT Distribution Neglect in Performance Evaluations E. Awtrey Journal Not Provided 2021 - 0 citations - Show abstract - Cite 49.8% topic match

47.3%

0.0

2017

[33] Star Power: The Effects of Hiring Different Types of Stars on Unit-Level Performance Pingshu Li and J. Guthrie https://doi.org/10.5465/AMBPP.2017.16608ABSTRACT 2017 - 0 citations - Show abstract - Cite 47.3% topic match

46.3%

0.0

1998

[34] Investment Talent and the Pareto Wealth Distribution: An Experimental Analysis Shiki Levy and H. Levy The Finance 1998 - 0 citations - Show abstract - Cite 46.3% topic match

43.7%

0.2

1968

[35] SIZE DISTRIBUTIONS OF FIRMS A STOCHASTIC MODEL L. Engwall https://doi.org/10.2307/3439308 1968 - 13 citations - Show abstract - Cite 43.7% topic match

40.7%

1.9

2018

[36] Top Earners: Cross-Country Facts A. Badel, ..., and Martin Nybom Microeconomics: Life Cycle Models & Behavioral Life Cycle Models eJournal 2018 - 12 citations - Show abstract - Cite - PDF 40.7% topic match

36.3%

1.1

2011

[37] Managing in a pareto world calls for new thinking P. Andriani and B. McKelvey https://doi.org/10.3917/MANA.142.0089 2011 - 15 citations - Show abstract - Cite 36.3% topic match

36.2%

1.2

2023

[38] Out of Shape: The Implications of (Extremely) Nonnormal Dependent Variables S. Certo, ..., and John R. Busenbark Organizational Research Methods 2023 - 2 citations - Show abstract - Cite 36.2% topic match

Investigates the implications of extremely nonnormal distributions in organizational research. Shows that dependent variables, including employee performance, demonstrate high skewness and kurtosis, impacting statistical analysis. Analyzes quantile regression as an effective method for modeling these distributions, but focus diverges to firm performance measures, not specifically employee salary links.

34.5%

0.0

2016

[39] A Bayesian Look at American Academic Wages: The Case of Michigan State University Majda Benzidia and M. Lubrano Journal Not Provided 2016 - 0 citations - Show abstract - Cite 34.5% topic match

32.4%

3.1

2016

[40] Zipf's Law, Pareto's Law, and the Evolution of Top Incomes in the U.S. Shuhei Aoki and Makoto Nirei Economic Growth eJournal 2016 - 26 citations - Show abstract - Cite - PDF 32.4% topic match

28.3%

0.0

2000

[41] Empirical Support for Asymmetry of the Distribution of Effort David L. Dickenson Journal Not Provided 2000 - 0 citations - Show abstract - Cite 28.3% topic match

Provides empirical evidence of non-Gaussian distribution of worker effort. Shows effort is negatively skewed in piece-rate work environments. Discusses implications for wage contracts and tournament-based compensation, without explicitly addressing Pareto distribution.

23.9%

0.0

2021

[42] Aspects of Pareto distributions J. Fellman Journal of Statistical and Econometric Methods 2021 - 0 citations - Show abstract - Cite 23.9% topic match

23.6%

3.1

2014

[43] The Empirical Reality of Entrepreneurship: How Power Law Distributed Outcomes Call for New Theory and Method G. Crawford, ..., and Benyamin Lichtenstein Entrepreneurship & Management eJournal 2014 - 32 citations - Show abstract - Cite 23.6% topic match

22.1%

1.4

2015

[44] A Static and Microfounded Theory of Zipf's Law for Firms and of the Top Labor Income Distribution F. Geerolf Journal Not Provided 2015 - 14 citations - Show abstract - Cite 22.1% topic match

18.3%

0.1

2015

[45] THE EMERGENCE OF OUTLIERS IN ENTREPRENEURSHIP: A SELF-ORGANIZED CRITICALITY FRAMEWORK G. Crawford Frontiers of entrepreneurship research 2015 - 1 citations - Show abstract - Cite 18.3% topic match

17.2%

0.0

2023

[46] Awareness of the consequences of right-skewed effort and productivity distributions in software development M. Jørgensen 2023 IEEE 25th Conference on Business Informatics (CBI) 2023 - 0 citations - Show abstract - Cite 17.2% topic match

Shows software productivity does not follow a normal distribution. It finds software development efforts and productivity follow a right-skewed distribution, having long tails toward higher values. It focuses on software development, not directly on general employee performance or Pareto distribution.

16.0%

0.7

2018

[47] Using maximum likelihood estimation methods and complexity science concepts to research power law-distributed phenomena G. Crawford and B. McKelvey https://doi.org/10.4337/9781785364426.00023 2018 - 5 citations - Show abstract - Cite 16.0% topic match

13.7%

29.4

2015

[48] What Do Data on Millions of U.S. Workers Reveal About Life-Cycle Earnings Risk? Fatih Guvenen, ..., and Jae Song ERN: Wealth 2015 - 293 citations - Show abstract - Cite - PDF 13.7% topic match

13.1%

0.0

2011

[49] ON-THE-JOB LEISURE AND ASYMMETRIC OBSERVED-EFFORT DISTRIBUTIONS * D. Dickinson Journal Not Provided 2011 - 0 citations - Show abstract - Cite 13.1% topic match

Shows empirical evidence of asymmetrically distributed observed worker effort. Finds significant negative skewness in observed effort; modal effort exceeds mean effort. Discusses implications for rank-order tournaments and optimal wage contracts, but focuses on effort instead of overall employee performance distributions.

12.6%

9.5

2017

[50] Zipf's Law, Pareto's Law, and the Evolution of Top Incomes in the United States† Shuhei Aoki and Makoto Nirei American Economic Journal: Macroeconomics 2017 - 71 citations - Show abstract - Cite 12.6% topic match

12.5%

1.0

1998

[51] Theories of the Distribution of Labor Earnings Derek A. Neal and S. Rosen https://doi.org/10.3386/W6378 1998 - 27 citations - Show abstract - Cite 12.5% topic match

11.6%

28.0

2013

[52] Skewness and Kurtosis in Real Data Samples M. Blanca, ..., and R. Bendayan Methodology: European Journal of Research Methods for The Behavioral and Social Sciences 2013 - 335 citations - Show abstract - Cite - PDF 11.6% topic match

11.3%

2.1

2006

[53] Firm Sizes: Facts, Formulae, Fables and Fantasies R. Axtell https://doi.org/10.2139/ssrn.1024813 2006 - 39 citations - Show abstract - Cite 11.3% topic match

11.0%

33.2

2021

[54] What Do Data on Millions of U.S. Workers Reveal About Lifecycle Earnings Dynamics? Fatih Guvenen, ..., and Jae Song Econometrica 2021 - 132 citations - Show abstract - Cite - PDF 11.0% topic match

10.7%

0.1

2007

[55] HOMEOSTATIC TENDENCIES OF FIRM-SIZE DISTRIBUTIONS AND THE EVOLUTION OF ECONOMIC SYSTEMS STABILITE DES DISTRIBUTIONS DE TAILLES D'ENTREPRISES ET EVOLUTION DES SYSTEMES ECONOMIQUES P. Winiwarter Journal Not Provided 2007 - 1 citations - Show abstract - Cite 10.7% topic match

10.5%

506.8

2007

[56] Power-Law Distributions in Empirical Data A. Clauset, ..., and M. Newman SIAM Rev. 2007 - 8891 citations - Show abstract - Cite - PDF 10.5% topic match

10.4%

0.4

2011

[57] Causes, Consequences and Dynamics of 'Complex' Distributions of Technological Activities: The Case of Prolific Inventors William Latham and C. Bas https://doi.org/10.4337/9780857930378.00016 2011 - 6 citations - Show abstract - Cite - PDF 10.4% topic match

9.7%

0.0

2019

[58] Star performers and team performance: the moderating roles of team cohesion and pay dispersion Olivier D. Boncoeur Academy of Management Proceedings 2019 - 0 citations - Show abstract - Cite 9.7% topic match

9.7%

0.9

2013

[59] Pareto Distributions and the Evolution of Top Incomes in the U.S Shuhei Aoki and Makoto Nirei Journal Not Provided 2013 - 10 citations - Show abstract - Cite 9.7% topic match

8.8%

0.1

2016

[60] Star Employees in Organizations: A Literature Review and Prospects Sha Kaiqing and Y. Zhong https://doi.org/10.16538/j.cnki.fem.2016.07.006 2016 - 1 citations - Show abstract - Cite 8.8% topic match

8.6%

0.0

2018

[61] Heroic Action and the Problem of Emergence:An Analytical Approach to Entrepreneurial Action Theory David M. Townsend and R. Hunt Academy of Management Proceedings 2018 - 0 citations - Show abstract - Cite 8.6% topic match

7.8%

0.7

2017

[62] Not All Non-normal Distributions Are Created Equal: Improved Theoretical and Measurement Precision Harry Joo, ..., and Kyle J. Bradley https://doi.org/10.5465/AMBPP.2017.10195ABSTRACT 2017 - 5 citations - Show abstract - Cite 7.8% topic match

6.5%

1.5

1960

[63] The Distribution of Ability and Earnings T. Mayer The Review of Economics and Statistics 1960 - 96 citations - Show abstract - Cite 6.5% topic match

6.4%

13.3

2015

[64] Stargazing: an integrative conceptual review, theoretical reconciliation, and extension for star employee research. Matthew L. Call, ..., and S. Thatcher The Journal of applied psychology 2015 - 129 citations - Show abstract - Cite 6.4% topic match

6.0%

0.0

2013

[65] IS THERE A SINGULAR DRIVER OF ENTREPRENEURSHIP ? POWER-LAW DYNAMICS OF ORGANIZATIONAL EMERGENCE G. Crawford Journal Not Provided 2013 - 0 citations - Show abstract - Cite 6.0% topic match

5.7%

None

[66] Power-law Distributions in Binned Empirical Data Yogesh Virkar and A. Clauset Journal Not Provided None - 65 citations - Show abstract - Cite Abstract: Many man-made and natural phenomena, including the intensity of earthquakes, population of cities, and size of international wars, are believed to follow power-law distributions. The accurate identification of power-law patterns has significant consequences for developing an understanding of complex systems. However, statistical evidence for or against the power-law hypothesis is complicated by large fluctuations in the empirical distribution's tail, and these are worsened when information is lost from binning the data. We adapt the statistically principled framework for testing the power-law hypothesis, developed by Clauset, Shalizi and Newman, to the case of binned data. This approach includes maximum-likelihood fitting, a hypothesis test based on the Kolmogorov-Smirnov goodness-of-fit statistic and likelihood ratio tests for comparing against alternative explanations. We evaluate the effectiveness of these methods on synthetic binned data with known structure and apply them to twelve real-world binned data sets with heavy-tailed patterns. 1. Introduction. Power-law distributions have attracted broad scientific interest [36] both for their mathematical properties, which sometimes lead to surprising consequences, and for their appearance in a wide range of natural and man-made phenomena, spanning physics, chemistry, biology, computer science, economics and the social sciences [21, 23, 33, 13]. Quantities that follow a power-law distribution are sometimes said to exhibit " scale invariance " , indicating that common, small events are not qualitatively distinct from rare, large events. Identifying this pattern in empirical data can indicate the presence of unusual underlying or endogenous processes, e.g., feedback loops, network effects, self-organization or optimization , although not always [29]. Knowing that a quantity does or does not follow a power law provides important theoretical clues about the underlying generative mechanisms we should consider. It can also facilitate statistical extrapolations about the likelihood of very large events [7]. 5.7% topic match

4.4%

0.2

2015

[67] Capturing complex processes of human performance Den Hartigh and Jan Rudolf Journal Not Provided 2015 - 2 citations - Show abstract - Cite 4.4% topic match

4.2%

3.1

2017

[68] Geometrically stopped Markovian random growth processes and Pareto tails Brendan K. Beare and Alexis Akira Toda arXiv: Econometrics 2017 - 22 citations - Show abstract - Cite 4.2% topic match

3.8%

0.0

2012

[69] Emerging Scalability and Extreme Outcomes in New Ventures: Power Law Distribution Analyses of Three Studies G. Crawford Ewing Marion Kauffman Foundation Research Paper Series 2012 - 0 citations - Show abstract - Cite 3.8% topic match

3.7%

0.0

2011

[70] Getting a grip on processes that govern the world Presenting R. Stelzer Journal Not Provided 2011 - 0 citations - Show abstract - Cite Abstract: Sometimes we are rudely awakened to this fact when a really catastrophic event happens such as an earthquake with unexpected strength at an unexpected location. That is the gist of non-traditional stochastic modeling: accounting for " unexpected events." Although such events cannot be predicted, they can be modeled. measurement errors, leading to the binomial distribution and in the limit, the Gaussian distribution. Many random physical phenomena are indeed governed by such distributions, a lot of theory has been developed for them and they have invaded engineering ranging from the design of electronic amplifiers and telecommunication links to helicopter control via Kalman filtering. Somehow, and thanks to the famous (Lindeberg-L ´ evy) central limit theorem, there is a belief that when you have the sum of a large number of presumably small effects, you automatically get a near-Gaussian distribution and that therefore all stochastic disturbances in engineering can be meaningfully modeled by Gaussian models.. . The truth, however, is much more complex. Many natural and human-made probabilistic phenomena do not adhere to a Gaussian distribution. This is already pretty evident from the properties of the latter. It has a very pronounced average value; the distribution is symmetric around that value and tapers off exponentially. Three or four " sigmas " away (sigma is a number equal to the standard deviation of the random variable) and the probability that the process has such a value is virtually nil. Already early on in the development of probability theory, the famous French mathematician L ´ evy defined a continuous distribution function for a new class of positive random variables, characteristic of some physical effects in spectroscopy and deviating from the Gaussian case. That new distribution has then been found useful for the modeling of economic effects such as the return on shares in the stock market. Pareto drew the attention of the economic community to these so-called " power law probability distributions, " a class of distributions that are described by a power law and hence have a " fat tail, " leading to statements such as " 80% of world's wealth is in 20% of the hands. " It seems that many meaningful distributions obey such laws: e.g., size of islands, Internet traffic, 1/f noise, size of sand particles, you name it – reason enough to give these distributions a great deal of attention! Probability theorists generalized the distributions discovered by L ´ … 3.7% topic match

3.0%

1.2

2015

[71] A consideration of normality in importance–performance analysis I. Lai and M. Hitchcock Current Issues in Tourism 2015 - 12 citations - Show abstract - Cite 3.0% topic match

2.6%

40.5

1989

[72] The unicorn, the normal curve, and other improbable creatures. T. Micceri Psychological Bulletin 1989 - 1456 citations - Show abstract - Cite 2.6% topic match

2.2%

7.0

2020

[73] Red Giants or Black Holes? The Antecedent Conditions and Multilevel Impacts of Star Performers Elham Asgari, ..., and Kip Kiefer Academy of Management Annals 2020 - 29 citations - Show abstract - Cite - PDF 2.2% topic match

1.9%

1.8

2008

[74] FRACTAL FLUCTUATIONS AND STATISTICAL NORMAL DISTRIBUTION A. Selvam Fractals 2008 - 30 citations - Show abstract - Cite - PDF 1.9% topic match

1.7%

0.1

2003

[75] A Life-Cycle Model of Income and Wealth Distribution Neng Wang Macroeconomics eJournal 2003 - 2 citations - Show abstract - Cite 1.7% topic match

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2003

[76] The generalized lognormal distribution as an income distribution Christian Kleiber and S. Scheid Journal Not Provided 2003 - 1 citations - Show abstract - Cite 1.2% topic match

1.1%

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2019

[77] Developing a Construct-Valid Measure of Workplace Aggression Oren R. Shewach Journal Not Provided 2019 - 0 citations - Show abstract - Cite 1.1% topic match

0.9%

0.0

2015

[78] Staffing Star Performers: Lessons from the National Football League (NFL) Brian J. Hoffman, ..., and D. Day https://doi.org/10.5465/ambpp.2015.13960symposium 2015 - 0 citations - Show abstract - Cite 0.9% topic match

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2010

[79] Evaluating Trade Reforms with Model with Heterogeneous Firms Kim J. Ruhl and T. Kehoe Journal Not Provided 2010 - 0 citations - Show abstract - Cite 0.6% topic match

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0.1

2016

[80] The Influence of Star Performers on Coordination and Performance:Does Type of Star Matter? Christopher M. Harris https://doi.org/10.15640/RCBR.V5N2A1 2016 - 1 citations - Show abstract - Cite Abstract: This study contributes to human capital research by focusing on star performers and a process through which they influence team performance. Star performers are important determinants of team functioning and performance. Using American collegiate basketball teams as a sample, this study examines two distinct measures of star performers and predicts different relationships between star performers, coordination, and performance based on the measure of a star performer. Coordination is examined as a process through which star performers influence unit performance. Evidence of coordination mediating the relationship between star performers and performance is found. Teams may have star performers who are disproportionately productive and valuable (Groysberg & Lee, 2008). While star performers are important to the performance of teams, it is also important for teams to function effectively in order to perform at a high level (e.g., Barrick, Stewart, Neubert, & Mount, 1998). Strategic human resource management frameworks indicate the relationship between human capital and performance works through behaviors that are important to the functioning of a team (e.g., Delery & Shaw, 2001; Wright & McMahan, 1992; Wright et al., 1994; Wright & Snell, 1991). Therefore, it is important to examine processes through which star performers influence the performance of teams. This study makes contributions to human capital research by assessing star performers in two different manners to examine their differential effects on team behaviors and performance. Additionally, this study examines coordination as process through which star performers influence the performance of teams. Star performers are strategically important, (Groysberg et al. 2008) therefore it is important to consider the influence that star performers have on team processes and performance. Research indicates that stars may have positive or negative influences on teams (e.g., Groysberg, Nanda, & Nohira, 2004). Stars that work well with fellow team members can enhance the functioning of the team (Groysberg & Lee, 2008). Stars may also demonstrate dominance in a team which would hamper team functioning (e.g., Driskell, Goodwin, Salas, & O’Shea, 2006; Groysberg et al., 2004). In this study, star performers are assessed in two distinct manners and their differential influences on team coordination and performance are examined. This study also extends human capital research by examining coordination as a process through which star performers influence team performance. This relationship is important to examine because people must use their human capital to create behaviors that lead to performance (Wright et al., 1994). Star performers are important to consider as they can influence the overall behaviors and performance of teams. These relationships are tested with a unique sample of NCAA men’s basketball teams. 1 School of Management, Texas Woman’s University, Denton, TX 76204, USA. 2 Review of Contemporary Business Research, Vol. 5(2), December 2016 Star Performers and Competitive Advantage According to the resource-based view of the firm, resources that are valuable, rare, inimitable, and nonsubstitutable create a competitive advantage for an organization (Barney, 1991). Following the resource-based view of the firm, differences in human capital, including the star performers of units create performance differences across units (e.g., Groysberg & Lee, 2008; Hitt, Bierman, Shimizu, & Kochar, 2001). Therefore, teams with star performers should outperform units without star performers (Groysberg & Lee, 2008). While it is important for teams to have star performers, it also important for these stars performers to exhibit the necessary behaviors for the unit to be successful (Delery & Shaw, 2001; Wright et al., 1994; Wright & Snell, 1991). Therefore, teams must select individuals that have the human capital necessary to exhibit the required behaviors (Wright et al., 1994). According to Wright et al. (1994), the potential of human capital is realized only to the extent that the possessors of the human capital choose to allow the unit to benefit from the human capital through their behaviors. The systems perspective of strategic human resource management proposes that the influence of people on performance acts as an input, throughput, out model (Wright and Snell, 1991). In this type of system it is proposed that characteristics of human resources (i.e., people) are the input and the human resources engage in role behaviors (throughput) that result in performance outcomes (output) (Wright & Snell, 1991). Therefore, it is indicated that people behaviors should mediate the relationship between characteristics of the workforce and performance (McMahan, Virick, & Wright, 1999; Wright & McMahan, 1992). As mentioned previously, this study examines coordination, which is defined as behavior that is intended to integrate and align the actions, knowledge, and objectives of interdependent members to achieve common goals (e.g., Brannick, Price, Prince, & Salas, 1995; Rico, Sanchez-Manzanares, Gil, & Gibson, 2008). Therefore, teams with star performers that enhance the coordination of other members of the team and increase team performance may develop a competitive advantage over other teams. Star Performers, Coordination, and Performance Today, organizations are more and more concerned with attracting and retaining individuals who are disproportionately productive and valuable (e.g., Groysberg & Lee, 2008; Groysberg et al., 2008). These star performers are important to organizations as they can have a large impact on the performance of organizations (Maister, 1993). According to Groysberg and colleagues (2008), two factors distinguish star performers from average performers. First, star performers are disproportionately more productive (Groysberg et al., 2008), making them more valuable to organizations (Groysberg & Lee, 2008). For example, star researchers have been found to be many times more productive than their colleagues (Ernst, Leptein, & Vitt, 2000; Narin & Breitzman, 1995). The ability and experience of star performers are assets that cannot be compensated for by less stellar performers or nonhuman assets (Kelley & Caplan, 1993; Narin, 1993). Second, star performers are more visible than average performers (e.g., Groysberg & Lee, 2008; Groysberg et al., 2008). That is, they receive more attention from competitors, clients, and the media. Similar to any industry, NCAA men’s basketball has star performers. One way to assess a star performer in NCAA men’s basketball is through the selection to an All American team. Each year, sportswriters vote on players to be selected to the Associated Press All American Team. Each year, 15 players are selected as All Americans. As it is rare to be selected as an All American, these players represent the most talented players. A basketball team with a highly talented All American player will most likely have an advantage over other teams. However, as playing basketball is a highly interdependent task, it is important for the All American player to work with teammates and coordinate their activities together in order to produce higher team performance. One item that may distinguish star performers is the people they work with (Groysberg et al., 2004). “Teammates often help stars by counseling them, coaching them, and serving as role models” (Groysberg et al., 2004 p. 6). If star performers are able to integrate and coordinate their activities with team members, the team most likely will perform at a higher level (Groysberg & Lee, 2008). This concept is similar with NCAA men’s basketball teams, a star player must work with his teammates in order for the team and most likely himself to perform at a higher level. Christopher M. Harris 3 As mentioned previously, players with a higher level of human capital in playing basketball will understand the need for players on the team to coordinate their activities in order for the team to perform at a higher level. A team with an All American has a player with a superior level of basketball human capital. Therefore, an All American player may facilitate the coordination of teammates in order for the team to perform at a high level. As a specific example, John Wall and DeMarcus Cousins from the University of Kentucky were each selected as All Americans for the 2009-2010 NCAA Division One Men’s Basketball season. The following quotes from them after being selected as All Americans demonstrate how they worked with their teammates to help the team perform at a high level. John Wall stated, “We had to learn a lot as freshmen and we were able to help our teammates along the way. This means a lot to both of us." Additionally, DeMarcus Cousins said, "This means a lot because all we really did was try to come in and help our teammates" (Associated Press, 2010). These quotes indicate that All American players can work to coordinate the activities of their teammates in order for the team to perform at a high level. Hypothesis 1: The positive relationship between a star player assessed as a team having an All American player and team performance is mediated by coordination. Another way to asses a star basketball player is via the percentage of a team’s points scored by the team’s highest scorer. In this situation, the highest scorer on the team may be viewed as the star player on the team. This is much different from an All American player, who is selected from all of the players in NCAA Division One men’s basketball. The player who scores the largest percentage of a team’s points may only indicate that the player is a star on his team. As basketball is a highly interdependent task, it is important for players to work together and coordinate their activities for the team to perform at a high level. If one player, is scoring a large percentage of a team’s points it may indicate that the team is not working well together 0.6% topic match

0.6%

0.3

1977

[81] Income Distributions in Two Experimental Economies R. Battalio, ..., and M. Reynolds Journal of Political Economy 1977 - 16 citations - Show abstract - Cite 0.6% topic match

0.4%

30.2

1982

[82] Authority, Control, and the Distribution of Earnings S. Rosen The Bell Journal of Economics 1982 - 1299 citations - Show abstract - Cite 0.4% topic match

0.3%

0.0

2015

[83] A Dynamical Systems Explanation of Talent Development in Sports J. R. D. Hartigh Journal Not Provided 2015 - 0 citations - Show abstract - Cite Abstract: For decades, research on talent development in sports has attempted to detect the mechanisms explaining excellent performance. Although researchers generally agree that different personal and environmental factors play a role (e.g., genetic endowment, practice, family support), how these factors combine to shape athletes’ routes to excellence remains largely undefined. In line with the proposition to apply a dynamical systems approach to study talent (Abbott, Button, Pepping, & Collins, 2005; Phillips, Davids, Renshaw, & Portus, 2010), we aimed to test whether typical properties of talent development can be explained by a dynamical systems model. For this aim, we built a model in which an athlete’s ability growth is dependent on relatively stable resources (genetic endowment) and variable resources (e.g., environmental variables). Furthermore, the variable resources are directly or indirectly influenced by the athlete’s ability and by each other, thereby shaping each other’s changes over time. Graphically, this can be envisioned as a dynamic network of talent-related components, and mathematically it corresponds to a coupled logistic growth equation (Van Geert, 1991). We simulated the model on a computer in order to see whether it generates typical properties of talent development and excellence. Simulations of many athletes revealed idiosyncratic trajectories towards excellence and a low correlation between early indicators and later excellence, which is often observed in sports (Abbott et al., 2005). Furthermore, the simulations showed that the distribution of performance attainments is highly right skewed across the (simulated) population of athletes, which is typical in virtually any sports (e.g., many Olympic swimmers won no medal, whereas Phelps won 22 medals). Our results thus suggest that excellence in sports develops out of dynamic network structures, which supports the proposition that the dynamical systems perspective has much to offer to the study of talent development. 0.3% topic match

0.3%

0.1

2006

[84] Modulated Branching Processes and Origins of Power Laws P. Jelenkovic and Jian Tan Journal Not Provided 2006 - 1 citations - Show abstract - Cite Abstract: Power law distributions have been repeatedly observed in a wide variety of socioeconomic, biological and technological areas, including: distributions of wealth,speciesarea relationships, populations of cities, values of compa nies, sizes of living organisms and, more recently, distributions of documents and visitors on the Web, etc. In the vast majority of these observations, e.g., city populations and sizes of l iving organisms, the objects of interest evolve due to the replica tion of their many independent components, e.g., births-deathsof individuals and replications of cells. Furthermore, the rates of replication of the many components are often controlled by exogenous parameters causing periods of expansion and contraction, e.g., baby booms and busts, economic booms and recessions, etc. In addition, the sizes of these objects oft en either have reflective lower boundaries, e.g., cities do not fall be llow a certain size, low income individuals are subsidized by the government, companies are protected by bankruptcy laws, et c; or have porous/absorbing lower boundaries, e.g., cities ma y degenerate, bankruptcy protection may fail and a company can be liquidated. Hence, it is natural to propose reflected modulated branching processes as generic models for many of the preceding observations of power laws. Indeed, our main results show that these apparently new mathematical objects result in power l aw distributions under quite general “polynomial Gärtner-Ellis” conditions. The generality of our results could explain the ubiquitous nature of power law distributions. Furthermore , an informal interpretation of our main results suggests that alternating periods of expansion and reduction, e.g., economic b ooms and recessions, are primarily responsible for the appearan ce of power law distributions. Our results also establish a general asymptotic equivalenc e between the reflected branching processes and the correspon ding reflected multiplicative processes. Furthermore, in the course of our analysis, we discover a duality between the reflected multiplicative processes and queueing theory. Esse ntially, this duality demonstrates that the power law distributionsplay an equivalent role for reflected multiplicative processes a s the exponential/geometric distributions do in queueing analy sis. 0.3% topic match

0.2%

0.8

2018

[85] Finding the Unicorn: Evidence-Based Best Practices for Improving Quantitative Measures Z. Miller Journal of park and recreation administration 2018 - 5 citations - Show abstract - Cite 0.2% topic match

0.2%

3.3

1997

[86] Citations and the Zipf-Mandelbrot Law Z. Silagadze Complex Syst. 1997 - 93 citations - Show abstract - Cite 0.2% topic match

0.2%

2.9

2011

[87] Pareto versus lognormal: a maximum entropy test. M. Bee, ..., and S. Schiavo Physical review. E, Statistical, nonlinear, and soft matter physics 2011 - 39 citations - Show abstract - Cite - PDF 0.2% topic match

0.1%

0.2

1999

[88] The Beta as a Model for the Distribution of Earnings S. Parker Bulletin of Economic Research 1999 - 5 citations - Show abstract - Cite 0.1% topic match

0.1%

0.0

2012

[89] The labour market and the distribution of income : an empirical analysis for Italy ∗ F. Clementi and M. Giammatteo Journal Not Provided 2012 - 0 citations - Show abstract - Cite 0.1% topic match

0.1%

0.0

2014

[90] A dynamic network model of expertise and exceptional performance in sports R. D. Hartigh and P. Geert Journal Not Provided 2014 - 0 citations - Show abstract - Cite Abstract: Introduction The study of expertise and exceptional performance covers a range from “beginner” to world-class performance. While developing sport expertise a variety of interacting internal and external performance factors are involved, which may differ between athletes (Phillips et al., 2010). The productivity distribution of athletes who ultimately reach expertise is highly right skewed. For instance, 30 male tennis players won 1 or 2 grand slams since the 90’s, and one exceptional player won 17 grand slams. We aim to propose a model that accounts for the multidimensionality and idiosyncratic developmental patterns of expert ability growth, as well as the highly skewed distribution of expert products at population level. Methods We departed from an existing dynamic model of ability growth (Van Geert, 1991), defining change based on three parameters: 1) stable resources (e.g., genetic constraints), 2) variable resources (e.g., coaching, motivation), and 3) proportion of change over time. However, given that the variable resources are also influenced by the ability growth and by each other, an athlete’s ability growth is better conceptualized as emerging from a dynamic network of connected components, defined as a set of coupled logistic growth equations (Van Geert et al., 2014). With computer simulations we first tested properties of individual expert ability growth. Second, we combined the network model with a model of product generation to test whether we could also predict the highly right skewed distribution of expert productivity. Results Model predictions based on simulations of many athletes revealed a wide variety of trajectories to reach expertise. Related to this, we found a low correlation between early indicators and later exceptional performance. Moreover, combining the network model with a (e.g., Poisson) product model we found highly right skewed distributions of expert productivity among the simulated athletes. Discussion The dynamic network model provided accurate predictions of key properties of expertise and exceptional performance (Simonton, 2001). This means that expertise and exceptional performance in sports likely emerge from a dynamic network model, which has important implications. For instance, the idiosyncratic developmental patterns and the lack of early indicators for later performance cast doubt on current practices of early talent detection and the search for (isolated) variables explaining expert performance. References Phillips E, Davids K, Renshaw I, Portus M (2010). Sports Med, 40, 271-283. Simonton DK (2001). Curr Dir Psychol Sci, 10, 39-43. Van Geert PLC (1991). Psychol Rev, 98, 3-53. Van Geert PLC, Den Hartigh RJR, Steenbeek HW, Van Dijk, MWG (Submitted). 0.1% topic match

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0.2

2018

[91] The Abundance of Star Teams: Antecedents of Heavy Tails in Team Productivity Distributions Kyle J. Bradley and Herman Aguinis Academy of Management Proceedings 2018 - 1 citations - Show abstract - Cite 0.1% topic match

0.1%

1.4

2014

[92] Star performers : task and contextual performance are components, but are they enough? Adelle Bish and B. Kabanoff https://doi.org/10.1111/1744-7941.12017 2014 - 15 citations - Show abstract - Cite - PDF 0.1% topic match

0.1%

2.8

2004

[93] War of the benchmark means: time for a truce J. Mashey SIGARCH Comput. Archit. News 2004 - 56 citations - Show abstract - Cite Abstract: For decades, computer benchmarkers have fought a War of Means. Although many have raised concerns with the geometric mean (GM), it continues to be used by SPEC and others. This war is an unnecessarymisunderstanding due to inadequately articulated implicit assumptions, plus confusio namong populations, their parameters, sampling methods, and sample statistics. In fact, all the Means have their uses, sometimes in combination. Metrics may be algebraically correct, but statistically irrelevant or misleading if applied to population distributions for which they are inappropriate. Normal (Gaussian) distributions are so useful that they are often assumed without question,but many important distributions are not normal.They require different analyses, most commonly by finding a mathematical transformations that yields a normal distribution,computing the metrics, and then back-transforming to the original scale. Consider the distribution of relative performance ratios of programs on two computers. The normal distribution is a good fit only when variance and skew are small, but otherwise generates logical impossibilities and misleading statistical measures. A much better choice is the lognormal (or log-normal) distribution, not just on theoretical grounds, but through the (necessary) validation with real data. Normal and lognormal distributions are similar for low variance and skew, but the lognormal handles skewed distributions reasonably, unlike the normal. Lognormal distributions occur frequently elsewhere are well-understood, and have standard methods of analysis.Everyone agrees that "Performance is not a single number," ... and then argues about which number is better. It is more important to understanding populations, appropriate methods, and proper ways to convey uncertainty. When population parameters are estimated via samples, statistically correct methods must be used to produce the appropriate means, measures of dispersion, Skew, confidence levels, and perhaps goodness-of-fit estimators. If the wrong Mean is chosen, it is difficult to achieve much. The GM predicts the mean relative performance of programs, not of workloads. The usual GM formula is rather unintuitive, and is often claimed to have no physical meaning. However, it is the back-transformed average of a lognormal distribution, as can be seen by the mathematical identity below. Its use is not onlystatistically appropriate in some cases, but enables straightforward computation of other useful statistics."If a man will begin in certainties, he shall end in doubts, but if he will be content to begin with doubts, he shall end with certainties." — Francis Bacon, in Savage. 0.1% topic match

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0.5

1976

[94] CHAPTER 2 A Function for Size Distribution of Incomes S. K. Singh and G. Maddala Journal Not Provided 1976 - 26 citations - Show abstract - Cite 0.0% topic match

0.0%

0.5

2010

[95] Models of statistical distribution K. Hart Anthropological Theory 2010 - 7 citations - Show abstract - Cite 0.0% topic match

0.0%

3.5

2004

[96] More "normal" than normal: scaling distributions and complex systems W. Willinger, ..., and Lun Li Proceedings of the 2004 Winter Simulation Conference, 2004. 2004 - 71 citations - Show abstract - Cite - PDF 0.0% topic match

0.0%

0.1

2008

[97] The exponentially truncated q-distribution: A generalized distribution for real complex systems H. M. Gupta and J. R. Campanha arXiv: Statistical Mechanics 2008 - 2 citations - Show abstract - Cite - PDF 0.0% topic match

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0.8

1966

[98] Exact moments of order statistics from the Pareto distribution H. J. Malik Scandinavian Actuarial Journal 1966 - 45 citations - Show abstract - Cite 0.0% topic match

0.0%

0.0

2014

[99] Zipf's Law for Firms: A Static and Microfounded Theory F. Geerolf Journal Not Provided 2014 - 0 citations - Show abstract - Cite 0.0% topic match

0.0%

0.3

2019

[100] A Stochastic Analysis of Firm Dynamics: Their Impact on the Firm Size Distribution Alexandre Reginster ERN: Market Structure (Topic) 2019 - 2 citations - Show abstract - Cite 0.0% topic match

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