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

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 com- pared to simple models. This paper considers mixture of Topp-Leone distributions under classical and Bayesian perspective based on com- plete sample. The new distribution which exhibits decreasing and up- side 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 pa- rameters of the model by using frequentist and Bayesian approaches. For Bayesian analysis, ve loss functions, namely the squared error loss function (SELF), weighted squared error loss function (WSELF), mod- ied squared error loss function (MSELF),