cdfbet
======

cumulative distribution function Beta distribution



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [P,Q]=cdfbet("PQ",X,Y,A,B)
    [X,Y]=cdfbet("XY",A,B,P,Q)
    [A]=cdfbet("A",B,P,Q,X,Y)
    [B]=cdfbet("B",P,Q,X,Y,A)




Arguments
~~~~~~~~~

:P,Q,X,Y,A,B five real vectors of the same size.
: :P,Q (Q=1-P) The integral from 0 to X of the beta distribution
  (Input range: [0, 1].)
: :Q 1-P
: :X,Y (Y=1-X) Upper limit of integration of beta density (Input
  range: [0,1], Search range: [0,1]) A,B : The two parameters of the
  beta density (input range: (0, +infinity), Search range:
  [1D-300,1D300] )
:



Description
~~~~~~~~~~~

Calculates any one parameter of the beta distribution given values for
the others (The beta density is proportional to `t^(A-1) *
(1-t)^(B-1)`.

Cumulative distribution function (P) is calculated directly by code
associated with the following reference.

DiDinato, A. R. and Morris, A. H. Algorithm 708: Significant Digit
Computation of the Incomplete Beta Function Ratios. ACM Trans. Math.
Softw. 18 (1993), 360-373.

Computation of other parameters involve a seach for a value that
produces the desired value of P. The search relies on the monotinicity
of P with the other parameter.

From DCDFLIB: Library of Fortran Routines for Cumulative Distribution
Functions, Inverses, and Other Parameters (February, 1994) Barry W.
Brown, James Lovato and Kathy Russell. The University of Texas.