On A Proposal For A New One-Parameter Survival Distribution

This article is devoted to a new one-parameter survival distribution which presents interesting features for statistical modeling. First, we show that it possesses very flexible probability density and hazard rate functions. Specifically, the probability density function can decrease with a heavy right tail, or be unimodal with an upside-down shape along with a possible light left tail. For its part, the hazard rate function has all monotonic forms; it can be increasing, constant or decreasing. The proposed distribution is also connected, in some senses, to the exponential, Weibull and linear failure rate distributions. This connection is highlighted by proving several first-order stochastic ordering results. Then, the moments are discussed both theoretically and numerically. A part is devoted to the related order statistics, with a focus on the two extreme statistics. For the statistical study, an estimate of the parameter is proposed using the maximum likelihood method. Then, the new distribution is fitted to two data sets to check its goodness of fit. Comparisons are made with other one-parameter distributions, namely the exponential, Lindley, one-parameter Weibull and one-parameter linear failure rate distributions, with favorable indicators for the distribution.