Non-central chi-square and gamma revisited
Harold Ruben · Communications in Statistics · 1974
The paper presents recursion relationships for the probability density and distribution functions of non-central chi-square and gamma random variables. Sum and interpolation formulae for the distribution functions are developed, and upper bounds obtained when the Interpolation formulae are used in truncated form. Finally, simple finite expansions for the distribution function of non-central chi-square with odd degrees of freedom are developed, and a simple expression for one distribution function of non-central chi-square with even degrees of freedom Is obtained in terms of Integrals involving the standardized normal distribution function and derivatives of the standardized normal density function.