A new compound extension of the Fr´echet distribution is introduced and studied. Some of its properties including
moments, incomplete moments, probability weighted moments, moment generating function, stress strength reliability
model, residual life and reversed residual life functions are derived. The mean squared errors (MSEs) for some estimation
methods including maximum likelihood estimation (MLE), Cram´er–von Mises (CVM) estimation, Bootstrapping (Boot.)
estimation and Kolmogorov estimates (KE) method are used to estimate the unknown parameter via a simulation study.
Two real applications are presented for comparing the estimation methods. Another two real applications are presented for
comparing the competitive models. The nonparametric Hill estimator under the breaking stress of carbon fibers is estimated
using the tail index (TIx) of the new model. Finally, a case study on reliability analysis of composite materials for aerospace
applications is presented. |
