The Properties of Topp Leone Exponentiated Inverse Weibull Distribution with Application to Survival Analysis

Abstract:

In this study, a new four-parameter lifetime distribution called the Topp Leone exponentiated inverse Weibull distribution was introduced. The graphs of the probability distribution function, cumulative density function and hazard function are presented to ascertain the shapes of the distribution. It is seen from the graphs that the shape of the distribution is skewed, symmetric, reversed J-shape, increasing, decreasing and bathtub and unimodal. A linear representation for the probability distribution function was carried out. Some mathematical properties of the distribution were presented such as moments, moment generating function, quantile function, survival function, hazard function. The distribution of order statistic was obtained. Estimation of the parameters by maximum likelihood method was discussed. An application to real-life of the distribution was presented and the result showed the fit and flexibility of the new distribution over some lifetime distributions considered. The analysis showed that the model is effective in fitting survival data.