## The Annals of Mathematical Statistics

### Saddle-point Methods for the Multinomial Distribution

I. J. Good

#### Abstract

Many problems in the theory of probability and statistics can be solved by evaluating coefficients in generating function, or, for continuous differentiable distributions, by an analogous process with Laplace or Fourier transforms. As pointed out for example by H. E. Daniels [2], these problems can often be solved by asymptotic series derived by the saddle-point method from integrals containing a large parameter. Daniels gave a form of saddle-point theorem that is convenient for applications to probability and statistics. In the present paper we extend the theorem in various directions and give some applications to distributions connected with the multinomial distribution, especially to the distribution of $\chi^2$ and to the distribution of the maximum entry in a multinomial distribution.

#### Article information

Source
Ann. Math. Statist., Volume 28, Number 4 (1957), 861-881.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177706790

Digital Object Identifier
doi:10.1214/aoms/1177706790

Mathematical Reviews number (MathSciNet)
MR93866

Zentralblatt MATH identifier
0091.14302

JSTOR