# 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 search for a value that produces the desired value of P. The search relies on the monotonicity 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.

## Examples

    x  = 0:0.1:1;
    y  = 1-x;

    A = 2*ones(x);
    B = 3*ones(x);

    [p,q]=cdfbet('PQ',x,y,A,B);
    plot2d2("gnn",[0:10]',p,5,"111","Repartition",[0,0,10,1])

x = 0:0.1:1; y = 1-x;

A = 2*ones(x); B = 3*ones(x);

[p,q]=cdfbet('PQ',x,y,A,B); plot2d2("gnn",[0:10]',p,5,"111","Repartition",[0,0,10,1])

## See Also

- cdfbin
- cdfchi
- cdfchn
- cdff
- cdffnc
- cdfgam
- cdfnbn
- cdfnor
- cdfpoi
- cdft