@stdlib/stats-base-dists-degenerate-pdf
v0.3.1TypeScript
Degenerate distribution probability density function (PDF).
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Published by The Stdlib Authors
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About stdlib...
Probability Density Function
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> [Degenerate distribution][degenerate-distribution] [probability density function][pdf] (PDF).
Strictly speaking, as a discrete distribution, a [degenerate][degenerate-distribution] has no [probability density function][pdf] (PDF). Extending the notion of a [PDF][pdf], we conceptualize the [PDF][pdf] of a [degenerate][degenerate-distribution] as an infinitely tall spike centered at mu. More formally,
where delta is the Dirac delta function.
Installation
``bash`
npm install @stdlib/stats-base-dists-degenerate-pdf
Usage
`javascript`
var pdf = require( '@stdlib/stats-base-dists-degenerate-pdf' );
#### pdf( x, mu )
Evaluates the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at mu.
`javascript
var y = pdf( 2.0, 8.0 );
// returns 0.0
y = pdf( 8.0, 8.0 );
// returns Infinity
`
#### pdf.factory( mu )
Returns a function for evaluating the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at mu.
`javascript
var mypdf = pdf.factory( 10.0 );
var y = mypdf( 10.0 );
// returns Infinity
y = mypdf( 5.0 );
// returns 0.0
y = mypdf( 12.0 );
// returns 0.0
`
Examples
`javascript
var pdf = require( '@stdlib/stats-base-dists-degenerate-pdf' );
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var opts = {
'dtype': 'float64'
};
var x = discreteUniform( 100, 0, 5, opts );
var mu = discreteUniform( 100, 0, 5, opts );
logEachMap( 'x: %d, µ: %d, f(x;µ): %0.4f', x, mu, pdf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/degenerate/pdf.h"
#### stdlib_base_dists_degenerate_pdf( x, mu )
Evaluates the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at mu.
`c`
double out = stdlib_base_dists_degenerate_pdf( 2.0, 3.0 );
// returns 0.0
The function accepts the following arguments:
- x: [in] double input value.[in] double
- mu: constant value of the distribution.
`c`
double stdlib_base_dists_degenerate_pdf( const double x, const double mu );
$3
`c
#include "stdlib/stats/base/dists/degenerate/pdf.h"
#include "stdlib/math/base/special/round.h"
#include
#include
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 result;
double mu;
double x;
int i;
for ( i = 0; i < 10; i++ ) {
x = stdlib_base_round( random_uniform( 0.0, 5.0 ) );
mu = stdlib_base_round( random_uniform( 0.0, 5.0 ) );
result = stdlib_base_dists_degenerate_pdf( x, mu );
printf( "x: %lf, µ: %lf, f(x;µ): %lf \n", x, mu, result );
}
}
`
*
Notice
This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-base-dists-degenerate-pdf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-degenerate-pdf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-degenerate-pdf/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-degenerate-pdf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-degenerate-pdf/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-degenerate-pdf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-degenerate-pdf/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-degenerate-pdf/main/LICENSE
[pdf]: https://en.wikipedia.org/wiki/Probability_density_function
[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution