A comparative study of bayesian and non-bayesian estimations for new generalized inverted weibull distribution

Abstract EN

This research proposes a new extension of the inverted Weibull distribution (IW) to provide a more adaptable distribution for modelling lifetime data, called the new inverted Weibull X-Gamma (NIWXG) distribution class.

Inverted Weibull, inverted Rayleigh, inverted exponential, X-Gamma inverted Rayleigh, and X-Gamma inverted exponential distributions are included as special sub-models in the suggested distribution.

For certain values of the parameters, the probability density and hazard rate curves are sketched in all feasible configurations.

Our main goal is to estimate its unknown parameters using non-Bayesian estimation techniques such as maximum likelihood estimation, Cramér-von-Mises estimation, least squares estimation, weighted least squares estimation, and Bayesian estimation under squared error loss function and LINEX loss function, as well as to derive some of its mathematical properties.

We utilize extensive numerical simulations for both small and big samples to compare the performances of the non-Bayesian and Bayesian estimators.

Based on the relative olute bias and root mean squared error criterion, the results demonstrate that the Bayesian estimation is the best estimation.