On the maximum and minimum for classes of univariate distributions

S. Nadarajah; I. E. Okorie

doi:10.1007/s13198-021-01078-y

On the maximum and minimum for classes of univariate distributions

S. Nadarajah
, I. E. Okorie

Mathematics

University of Manchester

Research output: Contribution to journal › Article › peer-review

Abstract

Given a random sample X₁, X₂, … , X_n, the distributions of min (X₁, X₂, … , X_n) and max (X₁, X₂, … , X_n) are of interest in many areas. We derive explicit expressions for moments of min (X₁, X₂, … , X_n) and max (X₁, X₂, … , X_n) for thirty four families of distributions, including the normal and Student’s t distributions. These results can be especially useful when data are scarce. The correctness of the expressions is checked by a simulation study. Applications to two engineering data sets are given.

Original language	British English
Pages (from-to)	290-309
Number of pages	20
Journal	International Journal of System Assurance Engineering and Management
Volume	12
Issue number	2
DOIs	https://doi.org/10.1007/s13198-021-01078-y
State	Published - Apr 2021

Keywords

Moments
Normal distribution
Student’s t distribution

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title = "On the maximum and minimum for classes of univariate distributions",

abstract = "Given a random sample X1, X2, … , Xn, the distributions of min (X1, X2, … , Xn) and max (X1, X2, … , Xn) are of interest in many areas. We derive explicit expressions for moments of min (X1, X2, … , Xn) and max (X1, X2, … , Xn) for thirty four families of distributions, including the normal and Student{\textquoteright}s t distributions. These results can be especially useful when data are scarce. The correctness of the expressions is checked by a simulation study. Applications to two engineering data sets are given.",

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On the maximum and minimum for classes of univariate distributions

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Keywords

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