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Distfun >> Distfun > Geometric > distfun_geopdf

distfun_geopdf

Geometric PDF

Calling Sequence

y = distfun_geopdf(x,pr)

Parameters

x :

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

pr :

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

y :

a matrix of doubles, the probability density.

Description

Computes the probability 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.

The function definition is:

Analysis of the random variable

The random variable X is the number of Bernoulli trials needed to get one success.

Compatibility Note : x belongs to the set {0,1,2,3,...}. This choice is compatible with Matlab and R. This is different from Scilab v5 grand(m,n,"geom"), which uses {1,2,3,...}.

Examples

// Test x scalar , pr scalar
computed = distfun_geopdf(3,0.5)
expected = 0.0625;

// Test with x expanded, with pr scalar
computed = distfun_geopdf([2 3],0.1)
expected = [0.081 0.0729];

//Test with x scalar, pr expanded
computed = distfun_geopdf(3,[0.2 0.4])
expected = [0.1024 0.0864];

//Test with both arguments expanded
computed = distfun_geopdf([3 4 8],[0.5 0.8 0.2])
expected = [0.0625 0.00128 0.033554432];

// Plot the function
scf();
x = 0:10;
y = distfun_geopdf(x,0.2);
plot(x,y,"ro-");
y1 = distfun_geopdf(x,0.5);
plot(x,y1,"go-");
y2 = distfun_geopdf(x,0.8);
plot(x,y2,"bo-");
xtitle("Geometric PDF","x","P(X=x)");
legend(["pr=0.2","pr=0.5","pr=0.8"]);

Bibliography

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

Authors


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