Approximation of stable and geometric stable distribution

Although there has been increased interest in the application of the stable and geometric stable distributions in economics and finance, further application has been limited because their probability density function does not have an explicit solution. In this paper, we present three analytic approximation methods — homotopy perturbation method, Adomian decomposition method, and variational iteration method — to resolve this problem. -- stable distributions ; geometric stable distributions ; fractional derivative and integral ; homotopy perturbation method ; adomian decomposition method ; variational iteration method