changfa
Advanced Member level 4
I need to calculate the mean of maximum of K i.i.d. Gaussian r.v.s., each with N(mu, sigma^2).
let M_K denote max(x1,x2,...,xK) and it is straight forward to show that the CDF of M_K is (F(x))^K where F(x) is the CDF of N(mu, sigma^2). Then the pdf of M_K is given by K*(F(x))^(K-1)*f(x).
The final step is to calculate the mean value of M_K as
E{M_K} = \int_{0}^{+oo} x * K*(F(x))^(K-1)*f(x) dx.
Does anyone know if there is close-form expression for this? or how to numerically calculate this integral in Matlab? (I tried but failed)
Thanks a lot!\]
let M_K denote max(x1,x2,...,xK) and it is straight forward to show that the CDF of M_K is (F(x))^K where F(x) is the CDF of N(mu, sigma^2). Then the pdf of M_K is given by K*(F(x))^(K-1)*f(x).
The final step is to calculate the mean value of M_K as
E{M_K} = \int_{0}^{+oo} x * K*(F(x))^(K-1)*f(x) dx.
Does anyone know if there is close-form expression for this? or how to numerically calculate this integral in Matlab? (I tried but failed)
Thanks a lot!\]