The Additive Lomax Power Lomax Distribution with Applications to Biomedical Data and Reliability Analysis

This paper is devoted to study a new five-parameter competing risks model called the additive Lomax power Lomax distribution. It is derived by considering a serial system with one component following the Lomax distribution and another following the power Lomax distribution. It has a very flexible hazard rate function accommodates different shapes, the most important shapes of them are the bathtub and the modified unimodal bathtub shapes. Some statistical properties of the proposed distribution such as quantile function, the mode, moments, the moment generating function, mean residual life, mean past lifetime, mean time to failure, entropy measures and order statistics are discussed. Moreover, the method of maximum likelihood is used to estimate the parameters, reliability and hazard rate functions of the model based on Type II censored samples. Also, the asymptotic confidence intervals of the parameters, reliability and hazard rate functions are obtained. A simulation study is carried out to evaluate the performance of the maximum likelihood estimates based on Type II censoring. The superiority of the proposed distribution over some known distributions is demonstrated through applications to biomedical data and reliability analysis.