The Weibull-Inverse Lomax (WIL) distribution with Application on Bladder Cancer

Abstract

In this paper, we introduced a four-parameter probability model called Weibull-Inverse Lomax distribution with decreasing, increasing and bathtub hazard rate function. The WIL distribution density function is J-shaped, positively skewed, and J-shaped in reverse. Some of the mentioned distribution’s statistical characteristics are provided including moments, order statistics, entropy, mean, variance, moment generating function, and quantile function. The method of maximum likelihood estimation was used to estimate the parameters of the model. The distribution’s importance is proved by its implementation to the bladder cancer data set. Goodness-of-fit of this distribution by various techniques demonstrates that the WIL distribution is empirically better for lifetime application.