PEGPW Polyno-Exponential Generalized Power Weibull Distribution with Applications to Failure Data

Abstract

The choice of an appropriate distribution for modelling data is often a major concern to researchers and practitioners. The Weibull distribution has been extensively used in reliability analyses due to its flexibility. However, owing to some of the drawbacks of the Weibull distribution, several researchers have proposed different modifications of it for modelling various types of data sets. This study proposes an extension of the Weibull distribution called the polyno-exponential generalized power Weibull distribution. Several properties of the new distribution, including the moments, moment generating function, stochastic ordering and order statistics, are studied. The plots of the density, failure rate and reverse hazard rate functions are obtained. The plots of the failure rate function exhibit various shapes including decreasing, increasing, constant, bathtub and upside-down bathtub shapes. Several estimation methods are used to obtain the parameter estimates of the distribution and their consistencies studied via Monte Carlo simulations. Empirical illustrations are used to show the usefulness and flexibility of the developed distribution. The results revealed that the new distribution can provide good parametric fit to given data sets.