
Hallo!
I would like to find P(X_1>X_2>X_3>X_4), where X_i are independent random variables with a Gaussian distribution, numerically solving the integral of the function f3 below:
f3=function(x,y,z){dnorm(z,mean = mu3,sd=sigma3)*dnorm(y,mean = mu2,sd=sigma2)*dnorm(x,mean = mu1,sd=sigma1)}
I tried the function integral3 of the package "pracma" withe the code below:
mu1=2
mu2=4
mu3=6
mu4=8
sigma1=1
sigma2=1
sigma3=1
sigma4=1
xmin < qnorm(0.000000000000001,mu1)
xmax < qnorm(0.999999999999999,mu4)
ymin=function(x){x}
ymax < qnorm(0.999999999999999,mu4)
zmin=function(x,y){y}
zmax < qnorm(0.999999999999999,mu4)
volume=integral3(f3, xmin, xmax ,ymin, xmax, zmin, zmax)
But I think that something is wrong.
To make a check setted all the means equal to 2 thus I expected a volume =1/24 but the value I obtained was 0.1666667.
Can someone give me a clue to solve the problem?
Thanks in advance,
elena
