On the maximum and minimum for classes of univariate distributions

S. Nadarajah () and I. E. Okorie
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S. Nadarajah: University of Manchester
I. E. Okorie: University of Manchester

International Journal of System Assurance Engineering and Management, 2021, vol. 12, issue 2, No 7, 290-309

Abstract: Abstract Given a random sample $$X_1, X_2, \ldots , X_n$$ X 1 , X 2 , … , X n , the distributions of $$\min \left( X_1, X_2, \ldots , X_n \right)$$ min X 1 , X 2 , … , X n and $$\max \left( X_1, X_2, \ldots , X_n \right)$$ max X 1 , X 2 , … , X n are of interest in many areas. We derive explicit expressions for moments of $$\min \left( X_1, X_2, \ldots , X_n \right)$$ min X 1 , X 2 , … , X n and $$\max \left( X_1, X_2, \ldots , X_n \right)$$ max X 1 , X 2 , … , 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.

Keywords: Moments; Normal distribution; Student’s t distribution (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13198-021-01078-y

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