# cdfbin

cumulative distribution function Binomial distribution

## Calling Sequence

    [P,Q]=cdfbin("PQ",S,Xn,Pr,Ompr)
                [S]=cdfbin("S",Xn,Pr,Ompr,P,Q)
                [Xn]=cdfbin("Xn",Pr,Ompr,P,Q,S)
                [Pr,Ompr]=cdfbin("PrOmpr",P,Q,S,Xn)

## Arguments

P,Q,S,Xn,Pr,Ompr

  six real vectors of the same size.

P,Q (Q=1-P)

  The cumulation from 0 to S of the binomial distribution. (Probability of S or fewer successes in XN trials each with probability of success PR.) Input range: [0,1].

S

  The number of successes observed. Input range: [0, XN] Search range: [0, XN]

Xn

  The number of binomial trials. Input range: (0, +infinity). Search range: [1E-300, 1E300]

Pr,Ompr (Ompr=1-Pr)

  The probability of success in each binomial trial. Input range: [0,1]. Search range: [0,1]

## Description

Calculates any one parameter of the binomial distribution given values for the others.

Formula 26.5.24 of Abramowitz and Stegun, Handbook of Mathematical Functions (1966) is used to reduce the binomial distribution to the cumulative incomplete beta distribution.

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

    	S = 0:1:10;
    	Pr  = 0.3 * ones(S);
    	Ompr  = 1-Pr;
    	Xn = 10*ones(S);
    	[p,q]=cdfbin('PQ',S,Xn,Pr,Ompr);
    	plot2d2("gnn",[0:10]',p,5,"111","Repartition",[0,0,10,1])

S = 0:1:10; Pr = 0.3 * ones(S); Ompr = 1-Pr; Xn = 10*ones(S); [p,q]=cdfbin('PQ',S,Xn,Pr,Ompr); plot2d2("gnn",[0:10]',p,5,"111","Repartition",[0,0,10,1])

## See Also

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