I have the following distribution for which I would like to have an
expression for the mean and variance:
P(x;n,o)=N(x) M(x)^(n-o) [ 1 - M(x) ]^(o-1)
with
N normal distribution with mean zero and variance s^2
M cumulative normal distribution with mean zero and variance s^2
n={1,2,3,4,...}
o={1,2,...,n}
I have no formal education in stat. and I am puzzled here. Just
evaluating E(X)=\int xP(x)dx gives me integrals that don't look like
I'm going anywhere.
If it helps, P is supposed to be the distribution of the o-th
descending ordered element from a set of size n of iid. normal rv with
mean zero and var s^2, e.g. o=1 => P is the distribution of max(z1,
z2, z3,...,zn) with all z ~ N.
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