Power Series Generalised Power Weibull Class of Distributions

Abstract

The power series generalised power Weibull class of distributions were developed in this study by compounding the power series family of distributions and the generalised power Weibull distribution. The statistical properties of this new class were derived. Maximum likelihood parameter estimators were derived for the parameters of the power series generalised power Weibull class of distributions. Four sub-families of distributions were developed from the power series generalised power Weibull class of distribution; the generalised power Weibull geometric distribution, generalised power Weibull Poisson distribution, generalised power Weibull binomial distribution and the generalised power Weibull logarithmic distribution. The hazard rate and probability density function plots of the four sub families of distributions showed that, they can model both monotonic and non-monotonic lifetime data. Monte Carlo simulations performed on these sub-distributions showed that, their estimators were consistent estimators. Application of these sub-distributions to failure data from air conditioning system of an aircraft showed that, the generalised power Weibull geometric distribution provides a better fit to the data. Also, the generalised power Weibull Poisson distribution provides a better fit to the data on service times of 63 aircraft.