On finite 3-component mixture of exponential distributions: Properties and estimation

To study reliability problems, life time and survival analysis, a new mixture model, called the 3-component mixture of the Exponential distributions, is introduced. This study is mainly concerned with the problem of investigating the different statistical properties of the newly developed 3-component mixture of Exponential distributions. Firstly, some basic properties of the 3-component mixture model are discussed. Secondly, we discuss hazard rate function, cumulative hazard rate function, reversed hazard rate function, mean residual life function, and mean waiting time function. Different measures of entropy and inequality indices are also discussed. Closed form expressions of the density functions of order statistics and their statistical properties are derived. Finally, the parameters of the proposed mixture distribution are estimated by making use of the maximum likelihood approach under complete and censored sampling. The results on maximum likelihood estimation are also supported through a simulation study and a real-life data