POWER SERIES INVERTED KUMARASWAMY DISTRIBUTION WITH APPLICATIONS TO LIFETIME DATA

Abstract

The inverted Kumaraswamy distribution has a drawback in modeling lifetime data which show non-monotone failure rates. Thus, a new class of distributions called power series inverted Kumaraswamy distribution was developed by compounding the inverted Kumaraswamy distribution with zero truncated power series distribution with the goal of making it more flexible. The new class of distributions were developed using the stochastic representation Z  min (T1,T2 ,...TN ) which is the time to the first failure of a system of identical components that are in a series. The statistical properties such as quantile, moments, moment generating function, stochastic ordering property and order statistics were developed for the new class of distributions. The maximum likelihood method was employed to develop estimators for the parameters. Special sub-distributions namely, Poisson inverted Kumaraswamy distribution, geometric inverted Kumaraswamy distribution, binomial inverted Kumaraswamy distribution and logarithmic inverted Kumaraswamy distribution were developed from the new class of distributions. The failure rate of the special distributions can be increasing, decreasing, bathtub and upside-down bathtub-shaped. Monte Carlo simulations were performed to examine the behavior of the estimators. The applications of the special distributions were illustrated using two lifetime data sets and the results revealed that among all the special distributions, the Geometric inverted Kumaraswamy distribution performs better.