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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.
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])
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