# FNChygecdf

FNChygecdf returns Fisher non-central hypergeometric cumulative distribution function

## Syntax

• Fcdf=FNChygecdf(x,M,K,n,odds)example
• Fcdf=FNChygecdf(x,M,K,n,odds, accuracy)example

## Description

This function calls function FisherNCHypergeometricpdf which is a translation into MATLAB of the corresponding C++ function of Fog (2008).

The notation which is used in FNChygecdf and the order of the arguments is the one of MATLAB hyge. The notation which is used inside FisherNCHypergeometricpdf is the original one of Fog.

 Fcdf =FNChygecdf(x, M, K, n, odds) Cumulative probability of getting 0 to x successes in n weighted drawns without replacement.

 Fcdf =FNChygecdf(x, M, K, n, odds, accuracy)

## Examples

expand all

### Cumulative probability of getting 0 to x successes in n weighted drawns without replacement.

Problem description.

% we have 500 balls in the urn
M  = 500;
%we extract 3 balls without replacement
n  = 3;
%initially, in the urn we have 250 red and 250 white balls
K  = M/2;
% red balls are ten times more likely to be extracted than the white balls
odds  = 10;
% We compute the cumulative probability of getting 0 1, or 2 red balls (in drawing
% the 2 balls without replacement).
x = 2;
fcdf = FNChygecdf(x,M,K,n,odds);
disp('prob of successes <=2;');
disp(fcdf);

## Input Arguments

### x — Number of red balls sampled. Scalar, vector or matrix.

Data Types: single|double

### M — Total number of balls in urn before sampling. Scalar, vector or matrix.

Data Types: single|double

### K — Initial number of red balls in the urn. Scalar, vector or matrix.

Data Types: single|double

### n — Total number of balls sampled. Scalar, vector or matrix.

Data Types: single|double

### odds — Probability ratio of red over white balls. Scalar, vector or matrix.

Data Types: single|double

### accuracy — accuracy of the calculations. Scalar.

The default value of accuracy is 1e-08.

Example: 1e-06 

Data Types: single|double

## Output Arguments

### Fcdf —Fisher' cdf values. Cumulative probability of drawing exactly x of a possible K items in n drawings without replacement from a group of M objects, when objects are from two weighted groups

The size of Wcdf is the common size of the input arguments. A scalar input functions as a constant matrix of the same size as the other inputs.

## References

Fog, A. (2008), Calculation Methods for Wallenius' Noncentral Hypergeometric Distribution, "Communications in Statistics - Simulation and Computation", Vol. 37, pp. 258-273.

## See Also

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