@stdlib/stats-base-dists-truncated-normal-pdf
v0.2.3TypeScript
Truncated normal distribution probability density function (PDF).
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Published by The Stdlib Authors
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Probability Density Function
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> [Truncated normal][truncated-normal-distribution] distribution probability density function (PDF).
A normally distributed random variable X conditional on a < X < b is called a [truncated normal][truncated-normal-distribution] distribution.
The [probability density function][pdf] (PDF) for a [truncated normal][truncated-normal-distribution] random variable is
where Phi and phi denote the [cumulative distribution function][cdf] and [density function][pdf] of the [normal][normal-distribution] distribution, respectively, mu is the location and sigma > 0 is the scale parameter of the distribution. a and b are the minimum and maximum support.
Installation
``bash`
npm install @stdlib/stats-base-dists-truncated-normal-pdf
Usage
`javascript`
var pdf = require( '@stdlib/stats-base-dists-truncated-normal-pdf' );
#### pdf( x, a, b, mu, sigma )
Evaluates the probability density function (PDF) for a [truncated normal][truncated-normal-distribution] distribution with lower limit a, upper limit b, location parameter mu, and scale parameter sigma.
`javascript
var y = pdf( 0.9, 0.0, 1.0, 0.0, 1.0 );
// returns ~0.7795
y = pdf( 0.9, 0.0, 1.0, 0.5, 1.0 );
// returns ~0.9617
y = pdf( 0.9, -1.0, 1.0, 0.5, 1.0 );
// returns ~0.5896
y = pdf( 1.4, 0.0, 1.0, 0.0, 1.0 );
// returns 0.0
y = pdf( -0.9, 0.0, 1.0, 0.0, 1.0 );
// returns 0.0
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = pdf( NaN, 0.0, 1.0, 0.5, 2.0 );
// returns NaN
y = pdf( 0.0, NaN, 1.0, 0.5, 2.0 );
// returns NaN
y = pdf( 0.0, 0.0, NaN, 0.5, 2.0 );
// returns NaN
y = pdf( 0.6, 0.0, 1.0, NaN, 2.0 );
// returns NaN
y = pdf( 0.6, 0.0, 1.0, 0.5, NaN );
// returns NaN
`
#### pdf.factory( a, b, mu, sigma )
Returns a function for evaluating the [probability density function][pdf] (PDF) for a [truncated normal][truncated-normal-distribution] distribution.
`javascript
var myPDF = pdf.factory( 0.0, 1.0, 0.0, 1.0 );
var y = myPDF( 0.8 );
// returns ~0.849
myPDF = pdf.factory( 0.0, 1.0, 0.5, 1.0 );
y = myPDF( 0.8 );
// returns ~0.996
`
Examples
`javascript
var randu = require( '@stdlib/random-base-randu' );
var pdf = require( '@stdlib/stats-base-dists-truncated-normal-pdf' );
var sigma;
var mu;
var a;
var b;
var x;
var y;
var i;
for ( i = 0; i < 25; i++ ) {
a = ( randu() * 80.0 ) - 40.0;
b = a + ( randu() * 80.0 );
x = ( randu() * 40.0 ) + a;
mu = ( randu() * 20.0 ) - 10.0;
sigma = ( randu() * 10.0 ) + 2.0;
y = pdf( x, a, b, mu, sigma );
console.log( 'x: %d, a: %d, b: %d, µ: %d, σ: %d, f(x;a,b,µ,σ): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), mu.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
}
`
*
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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[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[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-truncated-normal-pdf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-truncated-normal-pdf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-truncated-normal-pdf/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-truncated-normal-pdf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-truncated-normal-pdf/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-truncated-normal-pdf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-truncated-normal-pdf/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-truncated-normal-pdf/main/LICENSE
[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
[pdf]: https://en.wikipedia.org/wiki/Probability_density_function
[normal-distribution]: https://en.wikipedia.org/wiki/Normal_distribution
[truncated-normal-distribution]: https://en.wikipedia.org/wiki/Truncated_normal_distribution