CHEN FAMILY OF DISTRIBUTIONS WITH APPLICATIONS TO LIFETIME DATA

Abstract

Classical distributions are at times unable to provide a reasonable fit to certain forms of datasets, hence the need to generalize existing distributions to enhance their flexibility in the modeling of data. In recent times, much attention is focused on developing of new families of distributions for generalizing existing models. This is evident in the vast literature on modification and generalization of statistical distributions carried out by researchers. This study therefore developed generators of statistical distributions; the odd Chen and Chen generated families of distributions, using Chen distribution as the baseline model. Statistical properties of the developed families of distributions such as the quantile functions, moments, generating functions, order statistics and entropies were derived. The parameters of the generators were estimated and special distributions developed. Properties of the estimators for the parameters of some of the special distributions were investigated using Monte Carlo simulations. The usefulness of the special distributions in modeling real dataset was then demonstrated using four datasets. The developed distributions provided good fit to the given datasets and provided consistently better fit to these datasets than the existing competing models. Finally, the new distributions developed are capable of modeling both monotonic and non-monotonic failure rates, hence it is recommended that the distributions be considered, especially in situations were datasets exhibiting such failure rates are encountered.