Statistical Inference on 2-Component Mixture of Topp-Leone Distribution, Bayesian and non-Bayesian Estimation

Abstract

To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and
appealing as compared to simple models. This paper considers mixture of Topp-Leone distributions under classical and Bayesian perspective based on complete sample. The new
distribution which exhibits decreasing and upside down bathtub shaped density while the distribution has the ability to model lifetime data with decreasing, increasing and upside down
bathtub shaped failure rates. We derive several properties of the new distribution such as
moments, moment generating function, conditional moment, mean deviation, Bonferroni and
Lorenz curves and the order statistics of the proposed distribution. Moreover, we estimate the
parameters of the model by using frequentist and Bayesian approaches. For Bayesian analysis,
five loss functions, namely the squared error loss function (SELF), weighted squared error loss
function (WSELF), modified squared error loss function (MSELF), precautionary loss function (PLF), and K-loss function (KLF) and uniform as well as gamma priors are considered
to obtain the Bayes estimators and posterior risk of the unknown parameters of the model.
Furthermore, credible intervals (CIs) and highest posterior density (HPD) intervals are also
obtained. Monte Carlo simulation study is done to access the behavior of these estimators.
For the illustrative purposes, a real-life application of the proposed distribution to a tensile
strength data set is provided