# Accession Number:

## AD0641800

# Title:

## A BAYESIAN STUDY OF THE MULTINOMIAL DISTRIBUTION.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1966-10-01

# Pagination or Media Count:

## 40.0

# Abstract:

Lindley Ann.Math.Stat. 1964 studied the topic in the title. By using Fishers conditional- Poisson approach to the multinomial and the logarithmic transformation of gamma variables to normality, he showed heuristically that linear contrasts in the logarithms of the cell probabilities theta sub i are asymptotically jointly normal and suggested that the approximation can be improved by applying a correction to the sample. By studying the asymptotic series for the joint distribution, we have verified this assertion and found an improved correction procedure. A more detailed expansion is given for the distribution of a single contrast. In many problems linear functions of the theta sub i are of interest. The exact distribution for these is obtained. This has a density of a form familiar in the theory of serial correlation coefficients. A beta approximation is given. For three cells, a numerical example is given to show the merit of this approximation. The exact joint distribution of two linear functions of the theta sub i is also obtained and the theory is applied to a genetic linkage example. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability