Statistical Data analysis on the lifetime variable: statistical properties, estimation, residual life function and weighted moments

In this research the Beta-Gompertz Geometric (BGG) is proposed for data analysis of lifetime. The distribution is afive-parameter generalized issue of the Gompertz model which is entitled to Beta-Gompertz Geometric (BGG)distribution. It comprises some common lifetime distributions for example the Beta-Gampertz and generalized Gompertzdistributions that are as special sub-models. The proposed distribution is entirely flexible and it is able to apply foranalyzing survival data and reliability issues, effectively. Based on the it’s parameters, it has decreasing, increasing, andbathtub-shaped failure rate. The closed-form expressions for the density, cumulative distribution, hazard rate function,the kth order moment, moment generating function, Residual life function and Probability weighted moments asmathematical properties are provided in the distribution. We will consider the maximum likelihood estimation of theBGG’s parameters for an observed sample. Finally, we use a real dataset to explain the flexibility of the BGG distributionin an application.

Keywords:

Beta generator , Gompertz distribution , Beta Gampertz Geometric distribution , Maximum likelihood estimatior