SIZED-BIASED SAULEH DISTRIBUTION AND APPLICATIONS ON LIFETIME DATA SETS

Abstract

The weighted distributions are generally utilized in numerous fields like medication, nature, and reliability, and for the improvement of legitimate measurable models. Weighted distributions have great importance towards efficient statistical models. In this research paper we used Sauleh distribution and introduced a new weighted distribution named sized biased Sauleh distribution (SB-SD) and derived many of its properties like mean, variance, moment generating function, moments, reliability analysis, Lorenz, and Bonferroni curve, mean deviation, and order statistic for the newly derived model. To estimate the parameters of the SB-SD maximum likelihood estimations methos is used. Finally, we used the SB-SD in two lifetime data sets to check the applicability of the newly derived model. It is concluded that the SB-SD is more flexible as compared to the Sauleh and some other well-known distributions. Therefore, the proposed model can be used to estimate the probabilities that a patient will survive until a time, mean lifetime, mean residual lifetime, instantaneous failure rate and further survival measures for the lifetime data.