Type II Topp-Leone Bur XII distribution: Properties and applications to failure time data

Abstract

In this work, we present a three-parameter lifetime model named Type-II Topp-Leone Bur XII distribution developed using the Type-II ToppLeone (TIITL-G) family of distributions proposed by Elgarhy et al. (2018) which can be used to model reliability problems, fatigue life studies, and survival data has been studied. The newly developed model is more flexible and can be used to model data of various shapes of the hazard function. We derived explicit expressions for some of its statistical properties such as ordinary moments, generating function, incomplete moments, mean deviation, Bonferroni and Lorenz curve, Renyi entropy, Tsallis Entropy, order statistics, and stochastic ordering. The maximum likelihood estimation technique is used to estimate the parameters of the model. The performance of maximum likelihood estimators is assessed in terms of absolute bias, and standard error of simulation study. The applicability of the new model is illustrated by using two lifetimes’ data sets. The proposed distribution provides a reasonable better fit than some well-known distributions using the same criteria of comparison.