THE BETA TRANSMUTED POWER DISTRIBUTION: PROPERTIES AND APPLICATION

Abstract

In this this paper, we define and study a new generalization of the Power distribution and the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distribution taking Power distribution as the base distribution. The new distribution is called the beta transmuted Power (BTP) distribution. Some properties of the distribution such as moments, quantiles, mean deviation and order statistics are derived. The method of maximum likelihood is proposed to estimate the model parameters. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance-covariance matrix. A simulation study is conducted to study the performance of the estimators. The importance and flexibility of the new model is proved empirically using a real data set.