The Kumaraswamy-Burr Type III Distribution: Properties and Estimation

The Burr Type III distribution attracts special attention in life testing and reliability analysis as it is applied in several areas such as economics and environmetrics among others. A composite distribution of Kumaraswamy and Burr Type III distributions, referred to as Kumaraswamy-Burr Type III distribution, is introduced and studied. It contains some special well-known distributions, which are discussed in lifetime literature, such as the Burr Type III, exponentiated Burr Type III and Kumaraswamy-Burr Type XII, among several others. Some properties of the proposed distribution are studied including explicit expressions for the moments, the density functions of the order statistics, Rényi entropy, quantiles and moment generating function. The method of maximum likelihood is applied under Type II censored samples for estimating the model parameters, reliability and hazard rate functions. For different values of sample sizes, Monte Carlo simulation is performed to investigate the precision of the maximum likelihood estimates.