In this paper, it has been dealt with basic Gompertz distribution. The maximum likelihood, Bayes methods of estimation were used to estimate the unknown shape parameter. The failure rate (hazard) function with the least loss was found using different priors (Gamma, exponential, chi-square and triple prior) under symmetric loss function (Degroot loss function). A comparison was made about the performance of these estimators with the numerical solution that was found using expansion methods (Bernstein polynomial and power function) which was applied to find the failure rate function numerically. The proficiency test of the proposed methods was conducted with a number of test examples. Finally, for computations the Matlab (R2015b) is used.
The estimators of Gumbel type-II distribution parameter was set by using Maximum likelihood method (MLE) and Bayesian method, under many types of Loss functions; Linex Loss Function (LLF) Modified Linex Loss Function (MLLF), Balanced Linex Loss Function (BLLF), and Compound Linex Loss Function (CLLF) using Gamma prior.
One of the ways to compare the different estimators, and find the best method for estimation which used in this paper, Mean Squared Error (MSE) and Root Mean Square Error (RMSE), was used based on a Monte Carlo Simulation (MCS).
Finally, the discussion and illustrate of comparison results was showed and summarized in tables.
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