# T-function and V-function Calculator

## Calculates the T-function and V-function of the bivariate normal distribution.

 $\normal V(h,a)={\large\int_{\small 0}^{\hspace{25}\small h}\phi(x)\int_{\small 0}^{\hspace{25}\small ax}}\phi(y)dydx,\hspace{20}\phi(x)={\large\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}}\\T(h,a)+V(h,a)={\large\frac{1}{2\pi}}tan^{\tiny -1}a\\$
 percentile h coefficient a y=ax
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 $\normal T-function\ and\ V-function\ of\ bivariate\ normal\ distribution\\[10](1)\qquad V-function\\\hspace{30}V(h,a)={\large\int_{\small 0}^{\hspace{25}\small h}\phi(x)\int_{\small 0}^{\hspace{25}\small ax}}\phi(y)dydx,\hspace{20}\phi(x)={\large\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}}\\(2)\qquad T-function\\\hspace{30}T(h,a)={\large\frac{1}{\sqrt{2\pi}} \int_{\small 0}^{\hspace{25}\small a}\frac{e^{-h^2(1+x^2)/2}}{1+x^2} dx}\\(3)\qquad T(h,a)+V(h,a)={\large\frac{1}{2\pi}}tan^{\tiny -1}a\\$

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