A Novel Fréchet-Poisson Model: Properties, Applications under Extreme Reliability Data, Different Estimation Methods and Case Study on Strength-Stress Reliability Analysis

A new compound extension of the Fréchet 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\'{e}r--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.