Inverted Power Ishita Distribution and Its Application to Lifetime Data

Abstract

In this paper, a new distribution, named ‘the Inverted Power Ishita distribution’, was introduced.  It is an extension of the Ishita distribution and its capable of modelling real life data with upside down bathtub shape and heavy tails was introduced. Mathematical and statistical characteristics such as the quantile function, mode, moments and moment generating function, entropy measure, stochastic ordering and distribution of order statistics have been derived. Furthermore, reliability measures like survival function, hazard function and odds function have been derived. The method of maximum likelihood was used for estimating the parameters of the distribution. To demonstrate the applicability of the distribution, a numerical example was given. Based on the results, the proposed distribution performed better than the competing distributions, except for the inverse power rama. As the criterion values, the AIC, BIC, AICc values, for both the proposed distribution and the inverse power rama distribution are approximately the same, stating that both may be interchangeably used.