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distfun_binornd

Binomial random numbers

Calling Sequence

x = distfun_binornd(N,pr)
x = distfun_binornd(N,pr,[m,n])
x = distfun_binornd(N,pr,m,n)

Parameters

N :

a matrix of doubles , the total number of binomial trials . N belongs to the set {1,2,3,4,.......}

pr :

a matrix of doubles, the probability of getting success in a Bernoulli trial. pr in [0,1].

m :

a 1-by-1 matrix of floating point integers, the number of rows of x

n :

a 1-by-1 matrix of floating point integers, the number of columns of x

x:

a matrix of doubles, the random numbers, in the set {0,1,2,3,...}.

Description

Generates random variables from the Binomial distribution function.

Any scalar input argument is expanded to a matrix of doubles of the same size as the other input arguments.

If N<=2147483647, the algorithm is based on

Kachitvichyanukul, V. and Schmeiser, B. W. "Binomial Random Variate Generation.", Communications of the ACM, 31, 2 (February, 1988) 216.

If N is larger, then we invert the CDF.

Examples

// Check with expanded N
N = [10 100 1000 10000]
pr = 0.1
x = distfun_binornd(N, pr)

// Check with expanded pr
N =100
pr = [0.1 0.2 0.3 0.4]
x = distfun_binornd(N, pr)

// Check x = distfun_binornd(pr,v)
x = distfun_binornd(100,0.2,[4 5])

//Check mean and variance
N = 1000
pr = 0.3
n = 5000
x = distfun_binornd(N,pr,[1 n]);
Mx = mean(x)
Vx = variance(x)
[M,V] = distfun_binostat(N,pr)

// Check actual distribution
N=10;
pr=0.7;
K=10000;
h=scf();
x=distfun_binornd(N,pr,1,K);
distfun_inthisto(x);
h.children.children(1).children.background=-2;
x=0:N;
y=distfun_binopdf(x,N,pr);
plot(x,y,"ro-");
xtitle("Binomial Random Numbers","X","Density")
legend(["Empirical","Density"]);

Bibliography

http://en.wikipedia.org/wiki/Binomial_distribution

Authors


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