The Mirra Distribution For Modeling Time-To-Event Data Sets

Abstract

A two-parameter lifetime distribution named as two-parameter Mirra distribution (TPM) is proposed and studied in this article. The distribution is synthesized as a special finite mixture of exponential and gamma distributions. The name Mirra is given as a tribute to Mirra Alfassa, popularly known as The Mother. The proposed distribution is viewed as a generalization of xgamma distribution (Sen et al. 2016). Different distributional properties such as moments, shape, generating functions, etc., and important survival properties such as hazard rate function, mean residual life function, and stress-strength reliability are investigated. We propose method of moments and maximum likelihood for estimating the unknown parameter of the Mirra distribution. A sample generation algorithm along with a Monte Carlo simulation study is carried out to observe the pattern of the estimates for varying sample sizes. Finally, a real-life time-to-event data set is analyzed as an illustration, and Mirra distribution is compared with other standard lifetime distributions to check the suitability of the model. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021.