Classical and Bayesian estimation for the truncated inverse power Ailamujia distribution with applications

Abstract

In this study, we suggest the truncated version of the inverse power Ailamujia distribution, which is more flexible than other well-known distributions. Statistical properties of the new distribution are considered, such as moments, moment generating function, incomplete moments, quantile function, order statistics, and entropy. We discuss various methods of estimation, such as the method of maximum likelihood, methods of least squares and weighted least squares, the method of the maximum product of spacings, the method of Cramer and Von-Mises, methods of Anderson and Darling and right-tail Anderson and Darling, the method of percentiles, and the Bayesian method. Simulation is implemented to study the performance of estimates. We introduce two real data applications, showing that the new distribution can provide better fits than some other corresponding distributions.