E-Bayesian estimation for the parameters and hazard function of Gompertz distribution based on progressively type-II right censoring with application

E-Bayesian inference is of incremental significance in the area related to the reliability of industrial products dealing with censored data sets. In this article, based on the progressive Type-II right censored order statistics (PTIIRCOS), the E-Bayesian estimates (E-BE) for the parameters of Gompertz distribution (GD) and its hazard function are obtained and compared with the maximum likelihood (MLE) and Bayesian (BE) estimates. The squared error loss function (SE), linear-exponential loss function (LINEX), and Al-Bayyati loss function (ALB) are considered for the methods of BE and E-BE. Some properties for the E-BE estimates are discussed based on PTIIRCOS. Real data is established to clear the theoretical procedures. Akaike information criterion (AIC) is used to prove that GD is the best to model the data compared to other competitors and could potentially be very adequate in describing and modeling industrial products data. Finally, simulation study has been operated for comparing the E-BEs with the MLEs and BEs.