T函数与V函数
求2维标准正态分布的T函数和V函数。
| \(\normalsize V(h,a)={\large\int_{\small 0}^{\small h}\phi(x)\int_{\small 0}^{\small ax}}\phi(y)dydx,\hspace{20px}\phi(x)={\large\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}}\\ T(h,a)+V(h,a)={\large\frac{1}{2\pi}}tan^{\tiny -1}a\\ \) |
| \(\normalsize T-function\ and\ V-function\ of\ bivariate\ normal\ distribution\\ (1) V-function\\ \hspace{30px}V(h,a)={\large\int_{\small 0}^{\small h}\phi(x)\int_{\small 0}^{\small ax}}\phi(y)dydx,\hspace{20px}\phi(x)={\large\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}}\\ (2) T-function\\ \hspace{30px}T(h,a)={\large\frac{1}{\sqrt{2\pi}} \int_{\small 0}^{\small a}\frac{e^{-h^2(1+x^2)/2}}{1+x^2} dx}\\ (3) T(h,a)+V(h,a)={\large\frac{1}{2\pi}}tan^{\tiny -1}a\\ \) |
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