WNChygernd

WNChygernd random arrays from the Wallenius non central hypergeometric distribution.

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Syntax

  • r=WNChygernd(M,K,n,odds)example
  • r=WNChygernd(M,K,n,odds, mm)example
  • r=WNChygernd(M,K,n,odds, mm,nn)example
  • r=WNChygernd(M,K,n,odds, mm,nn,oo)example

Description

example

r =WNChygernd(M, K, n, odds) Generate a random number from Wallenius non central hypergeometric distribution.

example

r =WNChygernd(M, K, n, odds, mm) A difficult example which needs to avoid underflow/overflow.

example

r =WNChygernd(M, K, n, odds, mm, nn) Generate a 3D array of size mmxnnxoo of random number from Wallenius non central hypergeometric distribution.

example

r =WNChygernd(M, K, n, odds, mm, nn, oo) Comparison density and random numbers.

Examples

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  • Generate a random number from Wallenius non central hypergeometric distribution.

    • M=80; total number of balls n=10; number of balls taken odds=3; Prob. of red balls vs other color balls K=50; Number of red balls in the urn samplesize=100000; Sample size to extract 

    edges=(0:(n+1))';
% Generate a random number from the distribution above
x=WNChygernd(M,K,n,odds);
disp(x)

  • A difficult example which needs to avoid underflow/overflow.

    • M=8000; total number of balls n=2000; number of balls taken odds=3; Prob. of red balls vs other color balls K=5000; Number of red balls in the urn Generate an array of size 2x3x5 of random numbers from the distribution above 

    mm=2;   nn=3; oo=5;
rng(12345)
X=WNChygernd(M,K,n,odds);
disp(X)

  • Generate a 3D array of size mmxnnxoo of random number from Wallenius non central hypergeometric distribution.

    • M=800; total number of balls n=200; number of balls taken odds=3; Prob. of red balls vs other color balls K=500; Number of red balls in the urn Generate an array of size 2x3x5 of random numbers from the distribution above 

    mm=2;   nn=3; oo=5;
X=WNChygernd(M,K,n,odds, mm,nn,oo);
disp(X)

  • Comparison density and random numbers.

    • close all
M=100; % total number of balls
n=10;  % number of balls taken
odds=2; % Prob. of red balls vs other color balls
K=50; % Number of red balls in the urn
samplesize=100000; % Sample size to extract
edges=(0:(n+1))';
% Compute the density
Wpdf=WNChygepdf(edges(1:end-1),M,K,n,odds);
% Generate random numbers
x=WNChygernd(M,K,n,odds,samplesize);
% bar plot of theoretical and relative frequencies
freqANDdens=[(histcounts(x,edges-0.5)/samplesize)' Wpdf];
bar(edges(1:end-1),freqANDdens)
legend(["Theoretical density" "Empirical relative frequency"],'Location','best')
xlabel('Number of successes')
    Click here for the graphical output of this example (link to Ro.S.A. website).

    Input Arguments

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    M — Total number of balls in urn before sampling. Scalar.

    Data Types: single|double

    K — Initial number of red balls in the urn. Scalar.

    Data Types: single|double

    n — Total number of balls sampled. Scalar.

    Data Types: single|double

    odds — Probability ratio of red over white balls. Scalar.

    Data Types: single|double

    Optional Arguments

    mm — Length of first dimension. Scalar.

    Number of rows of the array which contains the random numbers.

    Example: 3

    Data Types: double

    nn — Length of second dimension. Scalar.

    Number of columns of the array which contains the random numbers.

    Example: 2

    Data Types: double

    oo — Length of third dimension. Scalar.

    Number of 3D slides of the array which contains the random numbers.

    Example: 5

    Data Types: double accuracy : accuracy of the calculations. Scalar. The default value of accuracy is 1e-10. Data Types - single|double Example - 1e-06

    Output Arguments

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    r —Random numnbers. Array of random numbers from the Wallenius non central hypergeometric distribution

    The size of rr is determined by the optional input parameters mm, nn, oo.

    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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