On an Induced Distribution and its Statistical Properties

TL;DR

This paper introduces a new statistical distribution, derives its properties, estimates its parameters numerically, and demonstrates its superior fit to real data compared to existing distributions using various statistical criteria.

Contribution

It proposes a novel distribution, derives its key properties, and shows its improved performance over existing distributions through empirical data analysis.

Findings

The new distribution's moments, entropy, and hazard functions are derived.

Maximum likelihood estimation requires numerical methods due to lack of closed form.

The proposed distribution outperforms Lindley, Garima, and Shanker distributions based on AIC, BIC, and K-S tests.

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 renyi 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 this distribution over some other existing distributions such as Lindley, Garima, Shanker and many more. AIC, BIC, -2loglikihood, K-S test suggest the proposed distribution works better than others distributions considered in this study.