A BURR X-PERKS DISTRIBUTION: PROPERTIES AND APPLICATIONS

Abstract

Probability distributions and associated properties have been used extensively over the years for modelling real life problems, however, most conventional distributions do not adequately analyze many of the skewed real-life datasets and therefore the need for compound or extended probability models. This paper presents a study on a new extension of the Perks distribution by adding one shape parameter to the conventional Perks distribution using the Burr X-G family of distributions. This study has derived and investigated some statistical properties of the Burr X-Perks distribution such as moments, moment generating function, the characteristics function, quantile function, survival function and hazard function. Some plots of the distribution and the reliability functions were generated and interpreted appropriately. The results from the curves show that the distribution is skewed with many shapes depending on the values of the parameters. The plot of the survival and hazard functions shows that the distribution can be used to model time-dependent events, where probability of survival decreases with time, while that of failure increases with time. The parameters of the new model have been estimated using the method of maximum likelihood estimation. The paper evaluated the performance of the proposed Burr X-Perks distribution using two real life datasets and the results revealed that the proposed Burr X-Perks distribution fits the two real life datasets better than the three other distributions considered in this study. 

Keywords: Burr X-G family, Perks distribution, Properties, Estimation and application.