Useful Methods for Generating Lifetime Distributions

In the practices of applied sciences such as engineering, finance, and medicine, amongst others, analyzing and modeling real phenomena is very crucial. In the recent literature, attempts have been made to propose new statistical distributions for modeling real phenomena of nature by adding one or more additional shape parameter(s) to the distribution of baseline random variable. The major contributions of these distributions are to obtain monotonic and non-monotonic shaped failure rates. In this study, new methods will be discussed to propose new lifetime distributions. In the very first approach, the cumulative hazard function will be utilized to introduce new lifetime distributions. In the second attempt, the log of cumulative hazard function will be discussed for generating new probability models. Also, some rules and conditions will also be provided that must be met before introducing new statistical distributions.