###
CONSTRUCTING ELEMENTARY PROCEDURES FOR INFERENCE

OF THE GAMMA DISTRIBUTION

###
TAKEMI YANAGIMOTO^{1} AND EIJI YAMAMOTO^{2}

^{1} *The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan*

^{2} *Department of Applied Mathematics, Okayama University of Science, Okayama 700, Japan*
(Received March 28, 1989; revised September 11, 1990)

**Abstract.**
The aim of the present paper is to construct a
series of estimators and tests in the one and the two sample problems
in the gamma distribution through the Kullback-Leibler loss. Some of
them are newly introduced here. When the approach is applied to the
case of the normal distribution, the well known estimators and tests
are derived. It is found that the conditional maximum likelihood
estimator of the dispersion parameter plays a key role.

*Key words and phrases*:
Chi-square test, conditional
inference, exponential family, *F*-test, Kullback-Leibler
loss.

**Source**
( TeX ,
DVI ,
PS )