Authors : Olanrewaju I. Shittu, Kazeem A. Adepoju and OlaOluwa S. Yaya
Abstract: Many useful properties of statistical distribution are revealed by transformation of random variables, however not many of the logic of beta distribution have been investigated by convolution techniques. This study investigates the statistical properties of the beta-exponential distribution defined by Nadarajah and Kotz. Specifically, it studies the distribution of the sum of two random variables from beta-exponential distribution using the convolution method. The probability density function (pdf) and the cumulative distribution (cdf) of the convoluted distribution were obtained. Also, derived are various statistical properties of the distribution which include moment, moment and characteristic generating function, skewness and kurtosis, hazard function and the entropy. The parameters of the distribution were estimated using the maximum likelihood method. The convoluted random variable was found to be unimodal and leptokurtic which makes it a more powerful distribution for analysis of financial data. The hazard function behaves in much the same way as that of Convoluted Beta-Weibull Distribution (CBWD).
Olanrewaju I. Shittu, Kazeem A. Adepoju and OlaOluwa S. Yaya, 2012. On the Convoluted Beta-Exponential Distribution. Journal of Modern Mathematics and Statistics, 6: 14-22.