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

where v > 0 is the degrees of freedom.

Usage

var logpdf = require( '@stdlib/stats/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 ~-3.447

y = mylogpdf( 1.0 );
// returns ~-1.838

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/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 );
}

C APIs

Usage

#include "stdlib/stats/base/dists/t/logpdf.h"

stdlib_base_dists_t_logpdf( x, v )

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

double out = stdlib_base_dists_t_logpdf( 0.5, 1.0 );
// returns ~-1.368

The function accepts the following arguments:

x: [in] double input value.
v: [in] double degrees of freedom.

double stdlib_base_dists_t_logpdf( const double x, const double v );

Examples

#include "stdlib/stats/base/dists/t/logpdf.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double x;
    double v;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( -10.0, 10.0 );
        v = random_uniform( 1.0, 100.0 );
        y = stdlib_base_dists_t_logpdf( x, v );
        printf( "x: %lf, v: %lf, ln(f(x;v)): %lf\n", x, v, y );
    }
}