Characteristic Properties for the Beta Exponentiated Weibull family

Abstract

The beta exponentiated Weibull family includes the beta Weibull, beta exponential, beta generalized exponential, beta Weibull and beta generalized Rayleigh distributions, among others. We provide a comprehensive treatment of new mathematical and statistical properties of the BEW distribution as a head member of this family of distributions. We derived an explicit mathematical formula for the mode. Impact of new parameters (a,b) on the corresponding first four moments are illustrated. Further, we discuss parametric characterizations for the failure-rate and associate mean residual life function. A general expression for the mean residual life function is derived. Simulation results are reported in several tables and graphs. The usefulness of some results is illustrated by applications to real data.