Saddlepoint approximations for multinomial distributions,with applications to the joint

Abstract

The saddlepoint approximation for the multinomial distribution is derived and expressed in terms of the corresponding generating function, so that the asymptotic formula of Good (1957) for the equiprobable multinomial distribution is generalized. Based on the multinomial argument, the representations and the saddlepoint approximation for the joint distribution function of order statistics from a continuous or discrete population are obtained. Numerical examples illustrate the great accuracy of the approximations.