Logarithm of Probability Density Function

Evaluate the natural logarithm of the probability density function (PDF) for a Student's t distribution.

The probability density function (PDF) for a t distribution random variable is

StartStartFraction 1 OverOver StartRoot nu EndRoot upper B left-parenthesis one-half comma StartFraction nu Over 2 EndFraction right-parenthesis EndEndFraction left-parenthesis 1 plus StartFraction x squared Over nu EndFraction right-parenthesis Superscript minus StartFraction nu plus 1 Over 2 EndFraction

where v > 0 is the degrees of freedom.

Usage

var logpdf = require( '@stdlib/math/base/dists/t/logpdf' );

logpdf( x, v )

Evaluates the natural logarithm of the probability density function (PDF) for a Student's t distribution with degrees of freedom v.

var y = logpdf( 0.3, 4.0 );
// returns ~-1.036

y = logpdf( 2.0, 0.7 );
// returns ~-2.841

y = logpdf( -1.0, 0.5 );
// returns ~-2.134

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

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

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

If provided v <= 0, the function returns NaN.

var y = logpdf( 2.0, -1.0 );
// returns NaN

y = logpdf( 2.0, 0.0 );
// returns NaN

logpdf.factory( v )

Returns a function for evaluating the natural logarithm of the PDF of a Student's t distribution with degrees of freedom v.

var mylogpdf = logpdf.factory( 1.0 );
var y = mylogpdf( 3.0 );
// returns ~-3.442

y = mylogpdf( 1.0 );
// returns ~-1.839

Examples

var randu = require( '@stdlib/random/base/randu' );
var logpdf = require( '@stdlib/math/base/dists/t/logpdf' );

var v;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = (randu() * 6.0) - 3.0;
    v = randu() * 10.0;
    y = logpdf( x, v );
    console.log( 'x: %d, v: %d, ln(f(x;v)): %d', x, v, y );
}