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Distfun >> Distfun > Geometric > distfun_geocdf

distfun_geocdf

Geometric CDF

Calling Sequence

p = distfun_geocdf(X,Pr)
p = distfun_geocdf(X,Pr,lowertail)

Parameters

X :

a 1x1 or nxm matrix of doubles, the number of Bernoulli trials after which first success occurs . X belongs to the set {0,1,2,3,......}

Pr :

a 1x1 or nxm matrix of doubles, the probability of success in a Bernoulli trial

lowertail :

a 1x1 matrix of booleans, the tail (default lowertail=%t). If lowertail is true (the default), then considers P(X<x) otherwise P(X>x).

p :

a nxm matrix of doubles, the probability.

Description

Computes the cumulative distribution function of the Geometric distribution function.

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

Examples

//Test with X scalar, Pr scalar
p = distfun_geocdf(3,0.5)
expected = 0.9375;

//Test with X expanded, Pr scalar
computed = distfun_geocdf([2 3],0.33)
expected = [0.699237 0.7984888];

//Test with X scalar, Pr expanded
computed = distfun_geocdf(3,[0.2 0.4])
expected = [0.5904 0.8704];

//Test with both the arguments expanded

computed = distfun_geocdf([3 4 8],[0.5 0.8 0.2])
expected = [0.9375 0.99968 0.8657823];

//Plot the function
scf();
Pr = 0.2;
Pr1 = 0.5;
Pr2 = 0.8;
for i=0:10
X = linspace(i,i+1,20);
y = distfun_geocdf(i,Pr);
plot(X,y,'r');
y = distfun_geocdf(i,Pr1);
plot(X,y,'g');
y = distfun_geocdf(i,Pr2);
plot(X,y,'b');
end
xtitle("Geometric CDF","x","P(X<x)");
legend(["Pr=0.2","Pr=0.5","Pr=0.8"]);

// See upper tail
p = distfun_geocdf(3,0.1)
lt_expected = 0.3439;
q = distfun_geocdf(3,0.1,%f)
ut_expected = 0.6561;
p+q

// See accuray in the upper tail
p = distfun_geocdf(100,0.5,%f)
expected = 3.944305e-31

Bibliography

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

Authors

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