Extension to Benrabia distribution with applications and parameter estimation

A new distribution is proposed in this artic;e using the area-biased as a special case of the weighted distributions. It is called the area-bias Benrabia distribution. The properties of this distribution are investigated, including moments, the moment generating function, the reliability functions, and many others. Several numerical studies are carried out, they show that the distribution is right-skewed and leptokurtic. We briefly describe different approaches of estimating the distribution parameters, namely, maximum likelihood, ordinary least-square and weighted least-square, maximum product of spacings, Cramer Von Mises and Anderson-Darling and compare them using extensive numerical simulations. We have shown that the distribution’s parameters are approximately unbiased and consistent. Two real data sets applications are run to show the goodness of fit of the suggested distribution. They illustrate that the proposed distribution fits these data better than other competence distributions.