Probability Density Function
Arcsine distribution probability density function (PDF).
The probability density function (PDF) for an arcsine random variable is
where a
is the minimum support and b
is the maximum support of the distribution. The parameters must satisfy a < b
.
Usage
var pdf = require( '@stdlib/stats/base/dists/arcsine/pdf' );
pdf( x, a, b )
Evaluates the probability density function (PDF) for an arcsine distribution with parameters a
(minimum support) and b
(maximum support).
var y = pdf( 2.0, 0.0, 4.0 );
// returns ~0.159
y = pdf( 5.0, 0.0, 4.0 );
// returns 0.0
y = pdf( 0.25, 0.0, 1.0 );
// returns ~0.735
If provided NaN
as any argument, the function returns NaN
.
var y = pdf( NaN, 0.0, 1.0 );
// returns NaN
y = pdf( 0.0, NaN, 1.0 );
// returns NaN
y = pdf( 0.0, 0.0, NaN );
// returns NaN
If provided a >= b
, the function returns NaN
.
var y = pdf( 2.5, 3.0, 2.0 );
// returns NaN
y = pdf( 2.5, 3.0, 3.0 );
// returns NaN
pdf.factory( a, b )
Returns a function
for evaluating the PDF of an arcsine distribution with parameters a
(minimum support) and b
(maximum support).
var myPDF = pdf.factory( 6.0, 7.0 );
var y = myPDF( 7.0 );
// returns Infinity
y = myPDF( 5.0 );
// returns 0.0
Examples
var randu = require( '@stdlib/random/base/randu' );
var pdf = require( '@stdlib/stats/base/dists/arcsine/pdf' );
var a;
var b;
var x;
var y;
var i;
for ( i = 0; i < 25; i++ ) {
x = ( randu()*20.0 )- 10.0;
a = ( randu()*20.0 )- 20.0;
b = a + ( randu()*40.0 );
y = pdf( x, a, b );
console.log( 'x: %d, a: %d, b: %d, f(x;a,b): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}