Parameter estimation methods for the Weibull‐Pareto distribution

Recently there has been a growing interest to study various estimation procedures to estimate the model parameters of the Weibull Pareto distribution (WPD). It is observed that the proposed distribution can be used quite effectively to model skewed data. They also proposed a modification of the maximum likelihood method (MML) to estimate the parameters of the WPD. The proposed methods showed a better performance from the standard maximum likelihood (ML) method. However, when the shape parameter c >>1, the modified ML method showed unforgettable large bias and standard deviation. In this article, we address some new properties and propose different methods of estimation of the unknown parameters of a WPD from the frequentist point of view. We briefly describe different frequentist approaches, namely, moments estimators, L‐moments estimators, percentile‐based estimators, least squares estimators, method of maximum product of spacings estimators, method of Cramér‐von‐Mises estimators, method of Anderson‐Darling estimators. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation and compare them with modified maximum likelihood estimation from the work of Alzaatreh et al (2013a). A real data set have been analyzed for illustrative purposes. Finally, bootstrap confidence intervals are obtained for the parameters of the model based on a real data set.