Topp-Leone modified Kies-G family of distributions: Properties, actuarial measures, inference and applications

Swetha, Potluri S S; Nagarjuna, Vasili B V

doi:10.21608/cjmss.2025.418412.1253

Topp-Leone modified Kies-G family of distributions: Properties, actuarial measures, inference and applications

Document Type : Original Article

Authors

Department of Mathematics, School of Advanced Sciences, VIT- AP University, Amaravati 522 241, India

10.21608/cjmss.2025.418412.1253

Abstract

We introduce a new two-parameter generalized family of distributions named the Topp-Leone Modified Kies-G family by combining the Topp-Leone-G and Modified Kies-G families. Several statistical properties of the proposed family were derived, including the moments, moment-generating function, order statistics, entropy, mean deviation, measures of inequality, and actuarial measures. A baseline distribution called the Topp-Leone Modified Kies exponential distribution is defined as a special member of this family. The proposed model supports the left and right-skewed, decreasing and decreasing-increasing-decreasing density forms, as well as the decreasing, increasing and bathtub hazard forms. A simulation study was carried out using different estimation techniques, including maximum likelihood, maximum product spacing, least squares, Cramer-Von-Mises and Anderson-Darling techniques, and the efficiency of the estimators was assessed. The practical applicability of the model is illustrated with three real-life datasets using various model adequacy and goodness-of-fit measures along with Vuong's test and leave-one-out log-likelihood. The findings indicate that the proposed model provides a better fit than the four well-known three-parameter models, demonstrating its applicability in reliability and survival analyses.

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