The Inverse Burr-Generalized Family of Distributions: Theory and Applications

Abstract

This paper presents a new class of generalized distributions based on the inverse Burr (Burr III) distribution. Statistical properties of the proposed family of distributions such as the density and cumulative distribution functions, survival and hazard rate functions, quantile, moments, moment generating function, probability weighted moments, Renyi entropy and distribution of order statistics are derived. The maximum likelihood estimation method is employed to obtain the parameter estimates of the family of distributions. A Monte Carlo simulation study is conducted in order to investigate the asymptotic behaviour of the parameter estimates of a sub-model from the proposed family of distributions. Finally, the utility of proposed family of distributions in lifetime data fittings is illustrated using two real data sets and the results obtained were compared to some existing non-nested models. Based on some model selection criteria and goodness of fit test statistics, it was evident that the sub-model from the proposed family of distributions performed reasonably better than the competitor distributions in fitting the two data sets.