A New Generalization of Transformed-Transformer Family of Distributions

Abstract

The development of generalized classes of distributions have attracted the attention of both theoretical and applied statisticians in recent times due to their exible statistical properties. In this study, the exponentiated generalized transformed-transformer family of distributions was proposed and studied. The statistical properties of the new family were derived and various sub-families were de ned. Some of the sub-families were used to develop the exponentiated generalized exponential Dagum, new generalized modi ed inverse Rayleigh and exponentiated generalized half logistic Burr X distributions. The statistical properties of the proposed distributions were studied and inferences were made on them. An extension of a sub-family of the exponentiated generalized transformed- transformer was developed by compounding it with the power series class to obtain the exponentiated generalized power series family of distributions. Monte Carlo simulations were performed to investigate the properties of the maximum likelihood estimators for the parameters of the developed distributions. The results revealed that the maximum likelihood estimators for the parameters were consistent. Applications of the proposed distributions were demonstrated using real data sets and their performance were com- pared to other known competing models. The proposed distributions showed greater

exibility and can be used to model di erent kinds of real data sets.