Probability of rth order statistic
- From: "Patrik" <hosanagar@xxxxxxxxx>
- Date: 3 Dec 2005 19:53:49 -0800
I have N variables X1, X2,..., Xn which are all iid random variables. I
want to figure out the probability that X1 is ranked "r" in ascending
order among the N items. The CDF of the distribution for these X
variables is F. I can think of 2 ways and I can't figure out which one
(if any) is correct:
1. The number of ways in which I can choose (r-1) variables to place
above X1 (i.e, having values less than X1) are (N-1) choose (r-1),
i.e., (N-1)C(r-1). Having chosen these variables, I have to set the
corresponding probabilities for values less than and greater than X1:
Pr(rank=r) = (N-1)C(r-1) * {F(X1)^(r-1)} * {(1-F(X1))^(n-r)
2. Someone else suggested I use the pdf of the rth order statistic
which is given by:
N!/{(N-r)!(r-1)!} * {F(X1)^(r-1)} * {(1-F(X1))^(n-r) * f(b)
Are either of these correct? I am inclined to use the first one because
the second one is really Prob (rth order stat = X1) which is different.
Maybe, I should use Prob(r-1 order stat < X1) * Prob(r+1 order stat >
X1) but do I even need to do that (can formula suffice). I'd appreciate
any input.
Thanks,
.
- Follow-Ups:
- Re: Probability of rth order statistic
- From: \"Luis A. Afonso\"
- Re: Probability of rth order statistic
- From: \"Luis A. Afonso\"
- Re: Probability of rth order statistic
- From: Richard Ulrich
- Re: Probability of rth order statistic
- Prev by Date: smaller errors after including correlations in the fit?
- Next by Date: Re: Probability of rth order statistic
- Previous by thread: smaller errors after including correlations in the fit?
- Next by thread: Re: Probability of rth order statistic
- Index(es):
Relevant Pages
|
