A New Topp-Leone Modified Kies-G Power Series Class of Distributions: Properties and Applications

Abstract

Many standard lifetime distributions cannot jointly represent skewed observations, tail variation, and non-monotonic hazard rates, particularly when failure is generated by an unobserved random number of competing risks. This paper introduces the Topp-Leone modified Kies-G power series class of distributions to address these modelling problems. The class combines baseline-distribution selection, modified Kies-G odds transformation, Topp-Leone shape control, and zero-truncated power-series compounding through a random-minimum construction. General expressions are derived for the distribution, density, survival, hazard, quantile, moments, moment-generating function, R\'enyi entropy, and order statistics. Five estimation methods are examined through Monte Carlo simulations under two parameter settings and sample sizes ranging from from 25 to 800. The special case of TL-MK-LLoGP distribution is applied to acute bone cancer survival times, airborne-transceiver repair times, and bank customer waiting times and compared with five flexible four-parameter models. It produces the smallest reported AIC and BIC values across the three datasets, although the magnitude of improvement varies. The proposed class therefore provides an additional modelling option for positive data requiring latent-risk interpretation and flexible hazard-rate behaviour.