Modifications of the Janardan Distribution and its Applications to Lifetime Data

Abstract

One of the recently developed probability distributions which are gaining popularity in modelling is a two-parameter Janardan distribution. However, Janardan distribution is discovered to be limited in controlling skewness and kurtosis which most lifetime data exhibit hence the need to modify the Janardan distribution through the method of parametrisation. To improve the usability and flexibility of the Janardan probability distribution, the study is designed to come out with three new probability distributions of which Janardan distribution is a baseline, establish the statistical properties of the new distributions as well as test their goodness of fit through the use of data. In line with the study objectives, three new distributions are developed through the method of parametrisation. These new distributions are Exponentiated Janardan (Three parameter distribution), Kumaraswamy Janardan (Four Parameter distribution) and Exponentiated Kumaraswamy Janardan (Five parameter distribution). Statistical properties such as PDF, CDF, Hazard rate, Survivor rate, Moments, Moment Generating function and MLE are established for each of the derived distributions. Empirical results reveal that all the derived models provide a better fit to all the considered sample datasets than the existing sub-models. Apart from the fact that these three derived distributions show superiority over Janardan Distribution and its sub model (Lindley distribution), the study further investigated the goodness of fit among the three new models. In comparing the three new distributions, the four-parameter Kumaraswamy Janardan (KJ) Distribution proves superiority in most cases. The researcher recommends that scholars should expand the statistical properties of the new distributions to bridge the research gap in mathematical computations. Also, industry experts in the field of reliability engineering, demography, actuary, etc; should use Kumaraswamy Janardan in modelling and predicting the reliability and hazard rate of their product since this distribution provides a robust hazard rate function.