MODIFICATIONS OF THE WEIGHTED WEIBULL DISTRIBUTION

Abstract

In modeling real-life events with respect to probability theory, two particular characteristics are considered, either the probability distribution is Flexible or the distribution is Tractable. Statistically, in order to retain the originality of the data, appropriate probability distribution needs to be employed rather than to transform the existing dataset. Classical distributions lack the ability to model and describe some important real-life events. Hence, the derived compound distributions are most appropriately employed to increase flexibility and capability to model real-life datasets. This study modified the weighted Weibull distribution with respect to Exponentiated Weighted Weibull and Geometric Weighted Weibull distributions which were obtained and derived having an interest in statistical theory. The shapes of the probability density function and hazard rate functions are investigated, as well as some structural statistical properties of the distribution. The study reports the use of the maximum likelihood estimation to determine unknown parameters by means of the Machov Chain Monte Carlo simulation and application using four illustrative datasets. The study shows the two derived modifications are obtained, which are the Geometric Weighted Weibull and the Exopnentiated Weighted Weibull. It is further reported that, the two derived distributions have superior performance compared with other modifications of the distributions. The The processes were performed using the R-Software. It is recommended that further study can be extended based on the derived distributions to construct autoregressive processes.