Computation of Density for A Linear Combination of –Generalized Normal Random Variables

Abstract

A computational procedure is presented for the approximation of the density of a linear combination of univariate -generalized normal random variables. (The -generalized normal random variable generalizes the ordinary normal one by replacing the power two in the exponent of the density by an arbitrary positive number.)

The procedure applies a truncated form of the Fourier Inversion Theorem to the power series expansion of the characteristic function of a -generalized normal random variable. Because of the unimodal nature of -generalized normal characteristic functions for ⩽ 2 and the oscillatory nature for > 2, much of the computational procedure divides into two corresponding parts. Complete error analysis and accuracy control in all computations are also presented.