A New Probability Heavy-Tail Model for Stochastic Modeling under Engineering Data

Abstract

The main aim of the paper is to propose and study a new heavy-tail model for stochastic modeling under engineering data. After studying and analyzing its mathematical properties, different classical estimation methods such as the ordinary least square, Cramér-von Mises, weighted least square, maximum likelihood, and Anderson–Darling estimation along with its corresponding left-tail and right-tail estimation methods are considered. Comprehensive numerical simulation studies are performed for comparing estimation methods in terms of some criterions. Three engineering and medical real-life data sets are considered for measuring the applicability flexibility of the new model and to compare the competitive models under uncensored scheme. Two engineering real-life data of them are also used to compare the classical methods. A modified Nikulin-Bagdonavicius goodness-of-fit is presented and applied accordingly for validation under censorship case. Finally, right censored lymphoma data set is analyzed under the modified statistic test for checking the validation of the reciprocal Weibull model in modeling the right censored data.