Exponentiated janardan distribution: A modification of janardan distribution and application to life time data.

Abstract

Applications of probability distributions have spread over the years from game of chance to all facet of life and disciplines. Due to quest of precision in modeling lifetime data, existing probability distributions are been improved upon through method of parameterization. This study introduced a new distribution called Exponentiated Janardan distribution of which Janardan distribution forms the baseline. This new distribution is a three-parameter distribution. Some statistical properties such as moments, MLE, survival/hazard rate are established. The proposed distribution was run on a number of life time datasets concurrently with the baseline distribution and the output result indicates that Exponentiated Janardan distribution produces smaller AIC value than the baseline distribution in all datasets considered. This indicates that Exponentiated Janardan distribution fits lifetime data more closely than Janardan distribution. The behavior of the pdf, survival function and hazard rate function are pictorially demonstrated. The role of each parameter in the proposed distribution is also pictorially demonstrated.