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Probability Density Function
Beta prime distribution probability density function (PDF).
The probability density function (PDF) for a beta prime random variable is
where α > 0
is the first shape parameter and β > 0
is the second shape parameter.
Usage
var pdf = require( '@stdlib/stats/base/dists/betaprime/pdf' );
pdf( x, alpha, beta )
Evaluates the probability density function (PDF) for a beta prime distribution with parameters alpha
(first shape parameter) and beta
(second shape parameter).
var y = pdf( 0.5, 0.5, 1.0 );
// returns ~0.385
y = pdf( 0.1, 1.0, 1.0 );
// returns ~0.826
y = pdf( 0.8, 4.0, 2.0 );
// returns ~0.301
If provided a x <= 0
, the function returns 0
.
var y = pdf( -0.1, 1.0, 1.0 );
// returns 0.0
y = pdf( 0.0, 1.0, 1.0 );
// returns 0.0
If provided NaN
as any argument, the function returns NaN
.
var y = pdf( NaN, 1.0, 1.0 );
// returns NaN
y = pdf( 0.0, NaN, 1.0 );
// returns NaN
y = pdf( 0.0, 1.0, NaN );
// returns NaN
If provided alpha <= 0
, the function returns NaN
.
var y = pdf( 0.5, 0.0, 1.0 );
// returns NaN
y = pdf( 0.5, -1.0, 1.0 );
// returns NaN
If provided beta <= 0
, the function returns NaN
.
var y = pdf( 0.5, 1.0, 0.0 );
// returns NaN
y = pdf( 0.5, 1.0, -1.0 );
// returns NaN
pdf.factory( alpha, beta )
Returns a function
for evaluating the PDF for a beta prime distribution with parameters alpha
(first shape parameter) and beta
(second shape parameter).
var mypdf = pdf.factory( 0.5, 0.5 );
var y = mypdf( 0.8 );
// returns ~0.198
y = mypdf( 0.3 );
// returns ~0.447
Examples
var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/float64/eps' );
var pdf = require( '@stdlib/stats/base/dists/betaprime/pdf' );
var alpha;
var beta;
var x;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
x = randu();
alpha = ( randu()*5.0 ) + EPS;
beta = ( randu()*5.0 ) + EPS;
y = pdf( x, alpha, beta );
console.log( 'x: %d, α: %d, β: %d, f(x;α,β): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
}