CONSTRUCTING ELEMENTARY PROCEDURES FOR INFERENCE OF THE GAMMA DISTRIBUTION

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

1The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan 2Department 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.