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distfun_betainc

Regularized Incomplete Beta function

Calling Sequence

y = distfun_betainc(x,z,w)
y = distfun_betainc(x,z,w,lowertail)

Parameters

x :

a matrix of doubles, the outcome. Should be in the [0,1] interval. If not, an error is generated.

z :

a matrix of doubles, the first shape parameter, z>=0.

w :

a matrix of doubles, the second shape parameter, w>=0.

lowertail :

a 1-by-1 matrix of booleans, the tail (default lowertail=%t). If lowertail is true (the default), then computes the integral from 0 to x otherwise from x to 1.

y :

a matrix of doubles, the output, y in [0,1].

Description

Computes the regularized Incomplete Beta function.

The Beta function is defined by

The incomplete Beta function is defined by

if x is in [0,1].

The (lower tail) regularized incomplete Beta function is defined by

if x is in [0,1].

The upper tail regularized incomplete Beta function is defined by

if x is in [0,1] where the upper tail of the incomplete Beta function is

The sum of the lower and upper tail is equal to 1 :

Examples

distfun_betainc(.5,(0:10)',3)

// Plot the function
z = 1;
w = 2;
x=linspace(0,1,100);
y = distfun_betainc(x,z,w);
plot(x,y)
xtitle("Regularized Incomplete Beta Function, z=1, w=2","x","Ix(z,w)");

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