On an Induced Distribution and its Statistical Properties

Abstract

In this study an attempt has been made to propose a way to develop new distribution. For this purpose, we need only idea about distribution function. Some important statistical properties of the new distribution like moments, cumulants, hazard and survival function has been derived. The R´enyi entropy, Shannon entropy has been obtained. Also ML estimate of parameter of the distribution is obtained, that is not closed form. Therefore, numerical technique is used to estimate the parameter. Some real data sets are used to check the suitability of the proposed distribution over some other existing one parameter lifetime distributions. The various diagnostic tools such as -2LL, AIC, BIC and K-S test shows that the proposed distribution provides better fit than other distributions for the considered data sets.