Length-Biased Loai Distribution: Statistical Properties and Application

Abstract

A new distribution is proposed in this paper using the length-biased dis- tribution as a special case of the weighted distributions. It is called the length-Bias Loai distribution. The properties of this distribution are inves- tigated, including moments, moment generating function, and the reliability functions and many others. Various numerical studies are carried out, they show that the distribution right skewed and leptokurtic. Different methods of estimation are used to estimate the distribution parameters. A simulation study is carried out to see the efficiency of the estimation methods, it shows that the distribution’s parameters are approximately unbiased and consis- tent. An application to a real data set is conducted to show the goodness of fit for the suggested distribution. It illustrates that the proposed distribution fits this data better than the other competence distributions.