The Weighted Xgamma Distribution: Properties and Application

Abstract

The weighted xgamma distribution, a weighted version of xgamma distribution (Sen et al. (2016) is introduced and studied in this article. A special non-negative weight function is considered to obtain the form of the weighted xgamma distribution which is shown as a generalization of xgamma distribution. The length biased xgamma distribution is then obtained as a special case of weighted xgamma density. Different distributional and survival properties of length biased xgamma distribution are studied along with the distributions of order statistics and entropy measure. We propose method of moments and maximum likelihood for estimating the unknown parameter of the length biased version. A sample generation algorithm along with a Monte Carlo simulation study is prepared to observe the pattern of the estimates for different sample sizes. Finally, a real life time-to-event data set is analyzed as an illustration and length biased distribution is compared with other standard lifetime distributions and length biased weighted exponential distribution to check the suitability of the model.