An example of a heavy tailed distribution

Abstract

We study some properties of the distribution function of a random variable of the form X = CD, where C and D are independent random variables. We assume that C is absolutely continuous and limited to a nite interval, such that its probability density function has de nite limits at the endpoints of the interval and D is exponentially distributed. We show that the tail function ¹ F(:) := 1 ¡ F(¢) is of regular variation and that the distribution function F is asymptotically equivalent to a log-gamma distribution. Then F can be considered as a heavy tailed distribution. It is also shown that it is contained is an special subclass of the subexponential distributions.