Length-Biased Benrabia Distribution with Applications

Abstract

The idea of weighted distributions is widely used in many fields, for ex- ample: medicine, ecology and reliability. They are more significant for mod- eling data when the base distributions are not proper or fit the data with less competence. Length biased distributions are special cases of the weighted distributions. In this paper, we propose a new generalization of Benrabia dis- tribution, called the length-biased Benrabia distribution. The recommended distribution’s various characteristics are deduced and thoroughly explored. Some numerical studies are implemented, they demonstrate that the distri- bution is skewed to the right with heavier tail than the normal distribu- tion. To estimate the distribution’s parameters six methods of estimation are employed. A simulation study is conducted shows that the estimators are approximately unbiased and consistent. Three data sets applications are performed, they show that the suggested distribution has the best fit for these data sets comparing to some competence distributions.