Linear Combination of Order Statistics Moments from Log-Extended Exponential Geometric Distribution with Applications to Entropy

Fatimah E. Almuhayfith (), Mahfooz Alam (), Hassan S. Bakouch, Sudeep R. Bapat and Olayan Albalawi
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Fatimah E. Almuhayfith: Department of Mathematics and Statistics, College of Science, King Faisal University, Alahsa 31982, Saudi Arabia
Mahfooz Alam: Department of Mathematics and Statistics, Faculty of Science and Technology, Vishwakarma University, Pune 411048, India
Hassan S. Bakouch: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Sudeep R. Bapat: Shailesh J. Mehta School of Management, Indian Institute of Technology Bombay, Mumbai 400076, India
Olayan Albalawi: Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi Arabia

Mathematics, 2024, vol. 12, issue 11, 1-15

Abstract: Moments of order statistics (OSs) characterize the Weibull–geometric and half-logistic families of distributions, of which the extended exponential–geometric (EEG) distribution is a particular case. The EEG distribution is used to create the log-extended exponential–geometric (LEEG) distribution, which is bounded in the unit interval (0, 1). In addition to the generalized Stirling numbers of the first kind, a few years ago, the polylogarithm function and the Lerch transcendent function were used to determine the moments of order statistics of the LEEG distributions. As an application based on the L-moments, we expand the features of the LEEG distribution in this work. In terms of the Gauss hypergeometric function, this work presents the precise equations and recurrence relations for the single moments of OSs from the LEEG distribution. Along with recurrence relations between the expectations of function of two OSs from the LEEG distribution, it also displays the truncated and conditional distribution of the OSs. Additionally, we use the L-moments to estimate the parameters of the LEEG distribution. We further fit the LEEG distribution on three practical data sets from medical and environmental sciences areas. It is seen that the estimated parameters through L-moments of the OSs give a superior fit. We finally determine the correspondence between the entropies and the OSs.

Keywords: Gauss hypergeometric function; order statistics; moments; recurrence relations; entropy; numerical results (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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