Analytical representation for positive /spl alpha/-stable densities

We present an analytical approximation to positive /spl alpha/-stable probability distribution functions, which in general do not possess a compact analytical form. Our approximation is based on decomposing a positive /spl alpha/-stable random variable into a product of a Pearson and another positive stable random variable. This decomposition allows one to approximate any positive stable pdf as a mixture of Pearson densities, hence providing an analytical representation. This representation allows one to employ maximum likelihood estimation and Bayesian techniques in the presence of positive /spl alpha/-stable noise or signals. The efficiency of the decomposition is demonstrated by simulation studies.