Annals of Mathematical Sciences and Applications

Volume 8 (2023)

Number 1

A note on moments of order statistics from the Pareto–Weibull distribution

Pages: 175 – 198

DOI: https://dx.doi.org/10.4310/AMSA.2023.v8.n1.a6

Authors

Z. Anwar (Department of Statistics and Statistics and Operations Research, Aligarh Muslim University, Aligarh, Uttar Pradesh, India)

Z. Ali (Department of Statistics and Statistics and Operations Research, Aligarh Muslim University, Aligarh, Uttar Pradesh, India)

M. Faizan (Department of Statistics and Statistics and Operations Research, Aligarh Muslim University, Aligarh, Uttar Pradesh, India)

M. A. Khan (Department of Statistics and Statistics and Operations Research, Aligarh Muslim University, Aligarh, Uttar Pradesh, India)

Abstract

The order random variables have been widely used, because of their applications in different areas, such as sports, seismology, reliability, quality control, actuarial science, etc. In this paper, we consider the Pareto–Weibull distribution. We derive the exact expressions for moments and recurrence relations, which are useful for obtaining various statistical characteristics of the given distribution. Further, we calculate the moments at different values of the parameters.

Keywords

order statistics, Pareto–Weibull distribution, single moments, double moments, triple moments, quadruple moments, recurrence relations, hypergeometric functions

2010 Mathematics Subject Classification

62E10, 62G30

Received 17 December 2022

Accepted 14 March 2023

Published 30 March 2023