Structural Properties of length biased Beta distribution of first kind

In this paper, a new class of Length-biased beta distribution of first kind is introduced. A Lengthbiased beta distribution of first kind is a particular case of the weighted beta distribution of first kind, taking the weights as the variate values has been defined. The characterizing properties of the model are derived. The estimates of parameters of Length-biased beta distribution of first kind are obtained by using method of moments. Also, a test for detecting the length-baisedness is conducted.