PCM Transformation: Properties and Their Estimation

Abstract

In the present piece of work, we are going to propose a new trigonometry based transformation called PCM transformation. We have been obtained its various statistical properties such as survival function, hazard rate function, reverse-hazard rate function, moment generating function, median, stochastic ordering etc. Maximum Likelihood Estimator (MLE) method under classical approach and Bayesian approaches are tackled to obtain the estimate of unknown parameter. A real dataset has been applied to check its fitness on the basis of fitting criterions Akaike Information criterion (AIC), Bayesian Information criterion (BIC), log-likelihood (-LL) and Kolmogrov-Smirnov (KS) test statistic values in real sense. A simulation study is also being conducted to assess the estimator’s long-term attitude and compared over some chosen distributions.