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Probabilistic Analysis of the Efficacy of Periodic Testing of Employees

Part of: Special processes Nonparametric inference Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Simeon M. Berman
Simeon M. Berman*
Affiliation:
New York University
*
∗Postal address: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA. Email address: sberman@cims.nyu.edu
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Abstract

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Some major companies have the policy of annually giving numerical scores to their employees according to their performance, firing those whose performance scores are below a given percentile of the scores of all employees, and then recruiting new employees to replace those who were fired. We introduce a probabilistic model to describe how this practice affects the quality of employee performance as measured over time by the annual scores. Let n be the number of years that the policy has been in effect, and let Fn(x) be the distribution function of the evaluation scores in year n. We show, under certain technical assumptions, that the sequence (Fn(x)) satisfies a particular nonlinear difference equation, and furnish estimates of the solution of the equation and expressions for the quantiles of Fn. The mathematical tools that are used include convex functions, difference equations, and extreme value theory for independent and identically distributed random variables.

Keywords

Convex functiondifference equationextreme valueperformance testquantile

MSC classification

Secondary: 60K99: None of the above, but in this section 62G32: Statistics of extreme values; tail inference 90B70: Theory of organizations, manpower planning
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 4 , December 2010 , pp. 1174 - 1190
Copyright
Copyright © Applied Probability Trust 2010 

References

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