The Greatest of a Finite Set of Random Variables
Abstract
The variables ξ 1, …, ξ n have a joint normal distribution. We are concerned with the calculation or approximation of max(ξ 1, …, ξ n). Current analyses and tables handle the case in which the ξ ı are independently distributed with common expected values and common variances. This paper presents formulas and tables for the most general case with n = 2. When n > 2, the problem becomes cumbersome. This paper presents formulas and tables that permit approximations to the moments in case n > 2. The moments are approximated by iteration of a three-parameter computation or, alternatively, through successive use of a three-parameter table, which is given. Recent applications of the theory are described.
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The finite-sample downward bias can be bounded.
“The finite-sample downward bias can be bounded; seeClark (1961).”
From Explainable AI Isn't Enough! Rethinking Algorithmic Contestability (2026) · cites this paper as Clark (1961)
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Discrete Choice Methods with Simulation
Train, K. E. (2001) · doi:10.1017/cbo9780511805271 · Cited by 7,784 · see citing works
Explainable AI Isn't Enough! Rethinking Algorithmic Contestability
Freiesleben, T., Meding, K., & König, G. (2026) · arXiv · doi:10.48550/arxiv.2605.16041
- Authors
- Clark, C. E.
- Affiliations
- System Development Corporation, Santa Monica, California
- Corresponding author
- Clark, Charles E.
- Venue
- Operations Research
- Published
- 1961-04
- Volume
- 9
- Issue
- 2
- Pages
- 145-162
- ISSN
- 0030-364X (ISSN-L)
- 1526-5463
- OpenAlex
- W2158750015
- Cited by
- 708
- References
- 0
- Citations by year
- 2026: 5 · 2025: 7 · 2024: 7 · 2023: 8 · 2022: 8 · 2021: 13 · 2020: 15 · 2019: 10 · 2018: 19 · 2017: 19 · 2016: 21 · 2015: 19 · 2014: 23 · 2013: 24 · 2012: 36
- FWCI
- 3.47
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Operations Research (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Social Sciences › Decision Sciences › Management Science and Operations Research › Probability and Risk Models
- Keywords
- maximum of random variables, multivariate normal distribution, bivariate normal distribution
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