Statistical Properties and Applications of Exponentiated Inverse Power Cauchy Distribution

Abstract

In this article, we have introduced the new distribution named exponentiated inverse power Cauchy distribution, which presents more flexibility in modeling a real lifetime dataset. The proposed distribution is analytically appealing and easy to work with and can be used efficiently to analyze the real data sets. Its probability density function can include various shapes according to the value of the parameters. Different explicit expressions for its quantile, survival, hazard and generating function, density function of the order statistics, cumulative hazard function, and failure rate function are provided. The model’s parameters are estimated by using the maximum likelihood estimation method, and we also obtained the observed information matrix. We have also constructed the asymptotic confidence intervals for the estimated parameters of the proposed distribution. We have illustrated the goodness-of-fit test and the application of the purposed distribution empirically through a real-life data set. All the computations are performed in R software (version 4.1.1). It is observed that the proposed distribution gets at least similar or a better fit than some selected distributions taken for comparison.