Approximations to noncentral distributions

Abstract Two methods for approximating the distribution of a noncentral random variable by a central distribution in the same family are presented. The first consists of relating a stochastic expansion of a random variable to a corresponding asymptotic expansion for its distribution function. The second approximates the cumulant generating function and is used to provide central χ 2 and gamma approximations to the noncentral χ 2 and gamma distributions.