On The Weighted BurrXII Distribution: Theory and Practice

We take an in-depth look at the weighted Burr-XII distribution. This distribu-tion generalizes Burr-XII, Lomax, and log-logistic distributions. We discuss the dis-tributional characteristics of the probability density function, the failure rate function,and mean residual lifetime of this distribution. Moreover, we obtain various statisti-cal properties of this distribution such as moment generating function, entropies, meandeviations, order statistics and stochastic ordering. The estimation of the distributionparameters via maximum likelihood method and the observed Fisher information ma-trix are discussed. We further employ a simulation study to investigate the behavior ofthe maximum likelihood estimates (MLEs). A test concerning the existence of size-biasin the sample is provided. In the end, a real data is presented and is analyzed usingthis distribution along with some existing distributions for illustrative purposes.