Re: A simple dice rolling problem

[snipped]
I have also seen the beta distribution used to
obtain binomial
probabilities.

That's a different kind of identity, different from
relationships
between
tail probabilities of different distributions.


There is a relation between the cdf of a binomial and
the cdf of a beta. For the dice problem, just type this
in EXCEL:

=betadist(5/6,850,151)

and you will find an answer accurate enough for
practical work. (See below for a further comment
on the accuracy.)

Given the properties of the incomplete beta function, you
could also do it this way: =1-betadist(1/6,151,850)

Because of the way EXCEL computes its functions, you'll
get better accuracy using BINOMDIST rather than
BETADIST for this example. Nevertheless, the identity
exists and may be useful in other situations.

Steve Oakley


If you are interested in those, you will find quite a
few on pp 1449-50
of the Peizer-Pratt paper (Dec. 1968) in equations
(7.1) to (7.19) in
the section on Recurrence Relations. The first few
are the ones
relating binomial terms to difference between the
cdfs of beta
distributions. That's the only copy of JASA before
2003 I kept. I
gave the rest of them to libraries in China. :)

-- Reef Fish Bob.

Now I'm going to have to grab a copy of your
paper.

Make sure you grab the right one. :) The 1992
paper only
high-lighted
the Binomial-F relation and pointed to the earlier
results I extracted
out
of Pratt's 1968 paper into one little section in my
1978 approximation
paper in JASA. The approximation formulas and
results are obsolete
now because exact results can be quickly computed,
but the
mathematical identities (5.1) - (5.6) in that paper
are the ones that
make some discrete distribution tables obsolete.

No relation given for the beta distribution tail
except to the F, but
the
relation between the Poisson tail and Chi-square
tail should be useful.

-- Reef Fish Bob.

.

Relevant Pages

  • Re: A simple dice rolling problem
    ... relationships between tail probabilities of different distributions. ... the cdf of a beta. ... the Binomial-F relation and pointed to the earlier ...
    (sci.stat.math)
  • Re: A simple dice rolling problem
    ... relationships between tail probabilities of different distributions. ... the cdf of a beta. ... the Binomial-F relation and pointed to the earlier ...
    (sci.stat.math)
  • Computer-Oriented Probabilities for Statistical Distributions (was Re: Findining a P value ...)
    ... > the twenty-five most commonly used statistical distributions. ... indeed excuse StaTable for its inadquacies as a program for computing ... missing the key ingredient for any p-value computation. ... > The one thing I find lacking is that it can't handle handle tail areas ...
    (sci.stat.math)
  • Re: MatLab randn and Simulation Step Numbers
    ... could have been a problem because on the tail of the distributions ... the chi square test is so sensitive that it can ... be thrown off by deviations from ideality. ...
    (sci.stat.edu)