A new Weibull Exponentiated Inverted Weibull Distribution for modelling positively-skewed data

Abstract

An Exponentiated Inverted Weibull Distribution (EIWD) has a hazard rate (failure rate) function that is unimodal, thus making it less efficient for modeling data with an increasing failure rate (IFR). Hence, the need to generalize the EIWD in order to obtain a distribution that will be proficient in modeling these types of dataset (data with an increasing failure rate). This paper therefore, extends the EIWD in order to obtain Weibull Exponentiated Inverted Weibull (WEIW) distribution using the Weibull-Generator technique. Some of the properties investigated include the mean, variance, median, moments, quantile and moment generating functions. The explicit expressions were derived for the order statistics and hazard/failure rate function. The estimation of parameters was derived using the maximum likelihood method. The developed model was applied to a real-life dataset and compared with some existing competing lifetime distributions. The result revealed that the (WEIW) distribution provided a better fit to the real life dataset than the existing Weibull/Exponential family distributions.