THE AUTHORS' ANSWER TO DISCUSSION BY YAN-GANG ZHAO AND HIDEKI IDOTA

Abstract

The authors thank Yan-Gang Zhao and Hideki Idota for their discussion. The answers are as follows;(1) We corrected the description of the definition of normalization according to their indication. And also we corrected the description related to the correlation coefficient ρ0,12 and the equation ƒ(χ1, χ2)(2) The cause of other indications seems to be the normalization. Joint probability density function for non-normal random variables was derived by bivariate normal distribution function. In the process of derivation, we used the normalization at any point of non-normal random variables. By this normalization the equivalent normal distribution can be gotten according to the point. Then the mean and standard deviation of the equivalent normal distribution are different at each point. But in the process of derivation, normal variate by normalization is transformed to standard normal variate, whose mean and standard deviation is zero and one respectively, even though the points are different. Finally the random variables included in the derived equation are standard normal variates and the original distribution function. So we think the derivation is correct.