Estimation of the Gompertz Distribution Parameters under Joint Progressive Censoring Data
Loading...
Date
2023
Journal Title
Journal ISSN
Volume Title
Publisher
Faculty of Sciences
Abstract
This thesis aims to estimate the Gompertz distributions parameters using the
joint progressive type-II censoring scheme. For the estimate problem, the likeli-
hood, Bootstrap, and Bayesian approaches are used. We employ various numeri-
cal methods, such Newton-Raphson, to solve the likelihood equations because the
resulting maximum likelihood estimators are not written in closed forms. Addi-
tionally, we take into account the Bayesian method for estimating the unknown
parameters while using independent gamma priors for the scale and shape pa-
rameters. We employ importance sampling and Metropolis-Hastings approaches
in the Bayesian analysis, which are based on symmetric and asymmetric loss
functions. Furthermore, credible intervals based on the Bayesian method and
confidence intervals based on asymptotic normality are presented. To compare
the performance of the proposed methods, a Monte Carlo simulation is run, and
real-life data is examined for illustrative purposes.