On the Flexibility of Topp Leone Exponentiated Inverse Exponential Distribution

Abstract

In this paper, we introduced a new continuous probability distribution called the Topp Leone exponentiated inverse exponential distribution with three parameters. We studied the nature of proposed distribution with the help of its mathematical and statistical properties such as quantile function, ordinary moments, moment generating function, survival function and hazard function. The probability density function of order statistic for this distribution was also obtained. We performed classical estimation of parameters by using the technique of maximum likelihood estimate. The proposed model was applied to two reallife datasets. The first data set has to do with patients with cancer of tongue with aneuploidy DNA profile and the second data set has to do with patients who were diagnosed with hypertension and received at least one treatment related to hypertension. The results showed that the new distribution provided better fit than other distributions presented. As such, it can be categorically said that the Topp Leone exponentiated inverse exponential distribution is good distribution in modeling survival data.