Order Statistics from Inverse Lomax Log-Logistic (IL-LL) Distribution

Zakir  Ali; Zaki  Anwar; Iftkhar  Khan

Authors

Zakir Ali Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, India
Zaki Anwar Department of Statistics and Operations Research, Aligarh Muslim University (Women’s College), Aligarh, India
Iftkhar Khan Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, India

Keywords:

Order statistics, inverse Lomax log-logistic distribution, single moment, product moments, hypergeometric functions, best linear unbiased estimator

Abstract

Random variables with order have found extensive use across various fields, including sports, seismology, reliability, quality control, actuarial science, and more. This study focuses on the inverse Lomax log-logistic distribution. Inverse Lomax log-logistic distribution is a flexible and robust model that exhibits several noteworthy statistical properties. Its probability density function is typically right-skewed and decreasing, making it suitable for modeling positively skewed data. We establish precise formulations for moments, providing valuable tools for determining diverse statistical properties of this distribution. We compute moments at various parameter values to enhance our understanding of the distribution. Further, these moments are used to determine the best linear unbiased estimators.

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