二変数ガンマ分布とその適用に関する研究(1) ―二変数指数分布の基礎理論―

Abstract

This study aims to develop the fundamental theory on two-variate gamma distributionfor its engineering application. The outline of the study is as follows:(1) Methods of estimation of the parameters included in the probability densityfunction of the distribution, the shape parameter in the marginal distribution of whichis the same in each other, are developed by using the techniques of maximum likeli-hood and moments. As the remarkable result, it is pointed Out that the estimator forcorrelation parameter is coincident with the usual definition of correlation coefficient bythe latter but not by the former.(2) The characters of the two-variate exponential distribution, which is a specialtype of the gamma distribution, is discussed theoretically and numerically.(3) For the convenience of engineering applications of the two-variate exponentialdistribution, numerical values of conditional probability under a given correlation para-meter are provided in a table.