A Bayesian and classical estimation of the new probabilistic Inverted Topp Leone Weibull distribution with application

Abstract

In this article, we present a new modification of the Weibull model with three parameters for analysing events in the real world, called the new Inverted Topp Leone Weibull distribution. The new model has many statistical advantages. The flexibility of the proposed model has been improved. The proposed model can be used to fit data with different shapes, it can be right skewed, left skewed, decreasing, curved and symmetric. The maximum likelihood approach and Bayesian estimation are used to estimate the distribution parameters. Three different loss functions are used for the Bayesian procedure. The calculations show the biases and estimated risks to obtain the best estimator. The bootstrap confidence intervals, the asymptotic confidence intervals, and the observed variance-covariance matrix are obtained. The Metropolis Hastings MCMC procedure is used for the calculations. We apply the composite distribution to two real data from the medical and engineering fields. The goodnessof-fit results show that it performs well compared to other distributions.