Logarithm of Probability Density Function

Arcsine distribution logarithm of probability density function (PDF).

The probability density function (PDF) for a 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 logpdf = require( '@stdlib/stats/base/dists/arcsine/logpdf' );

logpdf( x, a, b )

Evaluates the logarithm of the probability density function (PDF) for an arcsine distribution with parameters a (minimum support) and b (maximum support).

var y = logpdf( 2.0, 0.0, 4.0 );
// returns ~-1.838

y = logpdf( 5.0, 0.0, 4.0 );
// returns -Infinity

y = logpdf( 0.25, 0.0, 1.0 );
// returns ~-0.308

If provided NaN as any argument, the function returns NaN.

var y = logpdf( NaN, 0.0, 1.0 );
// returns NaN

y = logpdf( 0.0, NaN, 1.0 );
// returns NaN

y = logpdf( 0.0, 0.0, NaN );
// returns NaN

If provided a >= b, the function returns NaN.

var y = logpdf( 2.5, 3.0, 2.0 );
// returns NaN

y = logpdf( 2.5, 3.0, 3.0 );
// returns NaN

logpdf.factory( a, b )

Returns a function for evaluating the logarithm of the PDF for an arcsine distribution with parameters a (minimum support) and b (maximum support).

var mylogPDF = logpdf.factory( 6.0, 7.0 );
var y = mylogPDF( 7.0 );
// returns Infinity

y = mylogPDF( 5.0 );
// returns -Infinity

Notes

In virtually all cases, using the logpdf or logcdf functions is preferable to manually computing the logarithm of the pdf or cdf, respectively, since the latter is prone to overflow and underflow.

Examples

var randu = require( '@stdlib/random/base/randu' );
var logpdf = require( '@stdlib/stats/base/dists/arcsine/logpdf' );

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 = logpdf( x, a, b );
    console.log( 'x: %d, a: %d, b: %d, ln(f(x;a,b)): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}