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cumulative distribution function Beta distribution





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].)



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] )


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.


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

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


See also

  • cdfbin — cumulative distribution function Binomial distribution
  • cdfchi — cumulative distribution function chi-square distribution
  • cdfchn — cumulative distribution function non-central chi-square distribution
  • cdff — cumulative distribution function Fisher distribution
  • cdffnc — cumulative distribution function non-central f-distribution
  • cdfgam — cumulative distribution function gamma distribution
  • cdfnbn — cumulative distribution function negative binomial distribution
  • cdfnor — cumulative distribution function normal distribution
  • cdfpoi — cumulative distribution function poisson distribution
  • cdft — cumulative distribution function Student's T distribution
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