Re: Approxtn to LH Tail of NC F-Distbtn
- From: Barry W Brown <brownbar@xxxxxxxxx>
- Date: Mon, 17 Nov 2008 09:08:58 -0800 (PST)
On Nov 16, 8:51 pm, Outlier <MTBrenne...@xxxxxxxxx> wrote:
Hi,
Let F(x:n1,n2,L) denote the cdf for a non-central F-distribution with
degrees of freedom n1 and n2 and non-centrality parameter L. Let p be
some defined probability in the LH tail of the distribution (either
p=0.01, 0.05, or 0.10). (In other words, p is some missed detection
probability I wish to keep small).
Is there a decent formula for finding the approximate value of x
satisfying:
p = F(x:n1,n2,L)?
Equivalently, this can be cast in terms of the non-central Beta
distribution, i.e. is there a decent formula that gives the
approximate value of y satisfying
p = G(y:a,b,L)
where G is the cdf for the non-central Beta Distribution with a =
n1/2, b=n2/2, y = x*n1/(x*n1_n2)?
Thank you for any help you can provide as I can find absolutely
nothing in the literature on this.
Matt
Our free library cdflib (in Fortran) or interactive packaging as
STATTAB
has an inverse noncentral F. It uses a series approximation (exact if
all of the infinite number of terms included) to the noncentral F and
a
state of the art zero finder to invert the noncentral F. Both are
available
from
http://biostatistics.mdanderson.org/SoftwareDownload
.
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