README.md

Probability Density Function

Wald distribution probability density function (PDF).

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

$$f(x;\mu,\lambda)=\sqrt{\frac{\lambda}{2\pi x^3}}\, e^{-\frac{\lambda(x-\mu)^2}{2\mu^2 x}}$$

where µ > 0 is the mean and λ > 0 is the shape parameter.

Usage

var pdf = require( '@stdlib/stats/base/dists/wald/pdf' );

pdf( x, mu, lambda )

Evaluates the probability density function (PDF) for a Wald distribution with parameters mu (mean) and lambda (shape parameter).

var y = pdf( 2.0, 1.0, 1.0 );
// returns ~0.110

y = pdf( 0.5, 2.0, 3.0 );
// returns ~0.362

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

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

y = pdf( 1.0, NaN, 1.0 );
// returns NaN

y = pdf( 1.0, 1.0, NaN );
// returns NaN

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

var y = pdf( 2.0, 0.0, 1.0 );
// returns NaN

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

If provided lambda < 0, the function returns NaN.

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

If provided lambda = 0, the function evaluates the PDF of a degenerate distribution centered at mu.

var y = pdf( 2.0, 1.0, 0.0 );
// returns 0.0

y = pdf( 1.0, 1.0, 0.0 );
// returns Infinity

If provided x <= 0, the function returns 0.0.

var y = pdf( 0.0, 1.0, 1.0 );
// returns 0.0

y = pdf( -1.0, 1.0, 1.0 );
// returns 0.0

pdf.factory( mu, lambda )

Partially applies mu and lambda to create a reusable function for evaluating the PDF.

var mypdf = pdf.factory( 1.0, 1.0 );

var y = mypdf( 2.0 );
// returns ~0.110

y = mypdf( 0.5 );
// returns ~0.879

Examples

var uniform = require( '@stdlib/random/array/uniform' );
var logEachMap = require( '@stdlib/console/log-each-map' );
var EPS = require( '@stdlib/constants/float64/eps' );
var pdf = require( '@stdlib/stats/base/dists/wald/pdf' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 10, EPS, 10.0, opts );
var mu = uniform( 10, EPS, 10.0, opts );
var lambda = uniform( 10, EPS, 20.0, opts );

logEachMap( 'x: %0.4f, µ: %0.4f, λ: %0.4f, f(x;µ,λ): %0.4f', x, mu, lambda, pdf );

---

C APIs

Usage

#include "stdlib/stats/base/dists/wald/pdf.h"

stdlib_base_dists_wald_pdf( x, mu, lambda )

Evaluates the probability density function (PDF) for a Wald distribution with parameters mu (mean) and lambda (shape parameter).

double y = stdlib_base_dists_wald_pdf( 2.0, 1.0, 1.0 );
// returns ~0.110

The function accepts the following arguments:

• x: [in] double input value.
• mu: [in] double mean.
• lambda: [in] double shape parameter.

double stdlib_base_dists_wald_pdf( const double x, const double mu, const double lambda );

Examples

#include "stdlib/stats/base/dists/wald/pdf.h"
#include "stdlib/constants/float64/eps.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 lambda;
    double mu;
    double x;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        x = random_uniform( 0.0, 10.0 );
        mu = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
        lambda = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
        y = stdlib_base_dists_wald_pdf( x, mu, lambda );
        printf( "x: %lf, µ: %lf, λ: %lf, f(x;µ,λ): %lf\n", x, mu, lambda, y );
    }
}