二変数ガンマ分布とその適用に関する研究(2) ―二変数ガンマ分布の母数推定法―

Abstract

In the first report, the fundamental characteristics on two-variate gamma distribution, especiallytwo-variate exponential distribution were discussed. In this report, as the second step, the estimationof population parameters of two-variate gamma distribution are developed for the cases that asample from a total population is given and that a sample from a sub-population. In outline, thestudy is as follows:1) The estimating method based on a sample from a total population, every marginal distribu-tion of which has two parameters, is developed by using the technique of the moments method.2) The estimating method based on a sample from a sub-population, in which the domain ofindependent variable is defined as upper tail over a given value, is developed by using the techiqueof the maximum likelihood method.3) The applicability of the theory of two-variate gamma distribution is examined by apply-ing it to the data of river flows.