问题:对二元标准正态分布f(u,v)只对其中一个变量积分,对另一个变量赋值,求出这个值,程序如下
syms s t; %定义符号变量
f=@(rho,s,t)(1/sqrt(4*pi^2*(1-rho^2))*exp(-(s^2+2*rho*s*t+t^2)/(2*(1-rho^2))));
%定义二元标准正态分布的概率密度
s=-2.257930044773357;
rho=0.0115;
int(f,t,-inf,0.712283035751140) % 求值
结果如下
ans =
-(limit((2^(1/2)*pi^(1/2)*exp(s^2/(2*(rho^2 - 1)))*exp((rho^2*s^2)/(2*(rho^4 - 2*rho^2 + 1)))*exp(-(rho^4*s^2)/(2*(rho^4 - 2*rho^2 + 1)))*erf((2^(1/2)*t*(i/2))/((rho^2 - 1)*(1/(rho^2 - 1))^(1/2)) + (2^(1/2)*rho*s*(i/2))/((rho^2 - 1)*(1/(rho^2 - 1))^(1/2)))*(-i/2))/(1/(rho^2 - 1))^(1/2), t == -Inf) + (2^(1/2)*pi^(1/2)*exp(s^2/(2*(rho^2 - 1)))*exp((rho^2*s^2)/(2*(rho^4 - 2*rho^2 + 1)))*exp(-(rho^4*s^2)/(2*(rho^4 - 2*rho^2 + 1)))*erf((2^(1/2)*((400979701798895*i)/1125899906842624))/((rho^2 - 1)*(1/(rho^2 - 1))^(1/2)) + (2^(1/2)*rho*s*(i/2))/((rho^2 - 1)*(1/(rho^2 - 1))^(1/2)))*(i/2))/(1/(rho^2 - 1))^(1/2))/(2*pi*(1 - rho^2)^(1/2))
结果不是一个数,是一个函数,不知道问题出在了哪里!如果修改应该如何修改就可以得到积分的数!本人初学,请各位多指教!


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