A Survival Function of Proposed Versions of Three-Parameter Lindley Distribution (ThLD)

Abstract

The research aims to study one of the most important distributions used in estimating the survival function, the Lindley distribution, which is considered a mix of two continuous distributions. The Lindley distribution has a great ability to represent life and survival systems. We will study the Lindley distribution with three parameters because of its high flexibility in modeling life data. We proposed three versions of the three parameters of the Lindley distribution by making changes to the mixing weights and mixing parameters that are used in building the Lindley distribution function; we will denote these three proposed versions, respectively, as ThLD1st, ThLD2nd, and ThLD3rd. We will compute and prove some statistical properties for these three versions. We have used two methods for estimating the survival functions: the moments method and maximum likelihood estimation. We have compared the estimates of the survival functions using some criteria of accuracy (IMSE, -2 lnL, AIC, CAIC, and BIC). The simulation results have shown that (ThLD3rd) was superior at all sample sizes, followed by (ThLD2nd), (ThLD1st), and finally (ThLD). The moments method was superior to the sample size (10), and the maximum likelihood method was superior to the sample size (50, 100). The real data in the application also showed that the survival function estimate for ThLD3rd is the best one.