Logarithm of Probability Density Function

Uniform distribution logarithm of probability density function (PDF).

The probability density function (PDF) for a continuous uniform random variable is

$$f(x;a,b)=\begin{cases} \frac{1}{b - a} & \text{for } x \in [a,b] \\ 0 & \text{otherwise} \end{cases}$$

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/uniform/logpdf' );

logpdf( x, a, b )

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

var y = logpdf( 2.0, 0.0, 4.0 );
// returns ~-1.386

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

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

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 of a continuous uniform distribution with parameters a (minimum support) and b (maximum support).

var mylogPDF = logpdf.factory( 6.0, 7.0 );
var y = mylogPDF( 7.0 );
// returns 0.0

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/uniform/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 ) );
}

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C APIs

Usage

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

stdlib_base_dists_uniform_logpdf( x, a, b )

Evaluates the logarithm of the probability density function of a uniform distribution with parameters a (minimum support) and b (maximum support).

double out = stdlib_base_dists_uniform_logpdf( 2.0, 0.0, 4.0 );
// returns ~-1.386

The function accepts the following arguments:

• x: [in] double input value.
• a: [in] double minimum support.
• b: [in] double maximum support.

double stdlib_base_dists_uniform_logpdf( const double x, const double a, const double b );

Examples

#include "stdlib/stats/base/dists/uniform/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 a;
    double b;
    double x;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( -10.0, 10.0 );
        a = random_uniform( -20.0, 0.0 );
        b = random_uniform( a, a+40.0 );
        y = stdlib_base_dists_uniform_logpdf( x, a, b );
        printf( "x: %lf, a: %lf, b: %lf, ln(f(x;a,b)): %lf\n", x, a, b, y );
    }
}