Weighted Weibull Distribution: Properties and Estimation

We take a closer look at the weighted Weibull distribution. First, we study the structural properties of the probability density function, hazard rate, and mean residual lifetime functions of this distribution. We put forward the estimation for the parameters of the weighted Weibull distribution via maximum likelihood estimation technique. We also obtain expected Fisher's information matrix, as well as discuss the existence and uniqueness of the maximum likelihood estimates. With regard to Bayesian inference of the unknown parameters, we are using importance sampling technique to calculate Bayes estimates and the corresponding highest posterior density intervals. We perform a data analysis for illustrative purposes.