Marshall-Olkin Extended Inverse Weibull Distribution and Its Application

Abstract

Weibull distribution is the most popular distribution in wind speed energy literature. However, in real life, the wind speed data may not always modelled by Weibull distribution. An alternative in modeling wind speed data is the inverse Weibull distribution. Inverse Weibull distribution is modifications from the Weibull distribution with the transformation variables. Marshall and Olkin (1997) introduced an interesting method of adding a parameter to a well established distribution so we extend the Invers Weibull distribution by the Marshall-Olkin method (IWMO). The probability density function (pdf), cumulative distribution function (cdf), hazard rate, survival function, moment and quantiles of IWMO are derived. We also discuss the estimation of the model parameters by maximum likelihood. The IWMO distribution was applied to wind speed data. The results were given which illustrate the IWMO distribution and were compared to Weibull distribution and Inverse Weibull distribution. Model comparison using the log likelihood, AIC, and BIC showed that IWMO fit the data better than the other distributions.