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We present an analytical approximation to positive α-stable probability distribution functions, which in general do not possess a compact analytical form. Our approximation is based on decomposing a positive α-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 α-stable noise or signals. The efficiency of the decomposition is demonstrated by simulation studies.