Sum of Weighted Gamma Distribution: Properties and Applications in Reliability Engineering

Abstract

Applications of the lifetime continuous distributions in the reliability field are always in demand to improve the performance of electronic components. In this paper, we proposed a new method which is used to obtain a single-parameter lifetime distribution named “Sum of Weighted Gamma Distribution” (SWG distribution). The newly proposed distribution is obtained by weighing the gamma distribution with varying shape and constant scale parameters. The idea has been taken from the formation of the Lindley distribution, which is a mixture of exponential (with scale parameter ) and gamma (with shape parameter 2 and scale parameter ) distributions. Various mathematical properties of the SWG distribution have been derived. A few reliability and inequality measures, such as survival function, hazard rate, reversed hazard rate, cumulative hazard rate, Ginni indices, Lorenz and Bonferroni inequalities have been developed. Order statistics and upper record values from the SW-Gamma distribution have been studied. The parameter is estimated by using the method of maximum likelihood estimation (MLE), moreover, a simulation is conducted. Finally, the applications of the SWG distribution have been shown on three different lifetime data sets and compared with famous single-parameter lifetime distributions. It is shown that the SWG distribution is more flexible comparatively.