Comparison of Some Methods to Estimate the Hazard Function of the Generalized Gompertz Model Using Simulation

Abstract

This study examined the generalized Gompertz distribution, one of the most significant and popular failure models in reliability and life tests when the population is non-homogeneous. Two significant techniques for estimating the hazard function—the genetic method and the Nelder Mead algorithm—were employed once this model's significance, applications, and construction were thoroughly covered. The Monte Carlo method was utilized to simulate and compare these approaches because of its flexibility and cost-effectiveness in accounting for varying sample sizes (large, medium, and small) as well as predetermined values for the distribution and frequency parameters. Every time, try something new. This approach generates the data without using actual data. For the research model, both approaches have been shown to be adequate. Lastly, we anticipate that this model will incorporate additional intelligence algorithms, estimation techniques, and applications that are more broadly utilized across other domains.