The authors' answer to discussion by Yan-Gang Zhao and hideki idota

The authors thanks Yang-Gand Zhao and Hideki Idota fo 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 ρ_0,12 and the equation f (x₁,x₂) (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 functions. In the process of derivations, 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 standar normal variate, whoes mean and standard deviation is zero and one respectively, even though the points are different. Finally the random variables included in the derived equaltion are standard normal variates and the original distribution functions. So we think the derivation is correct.