Truncated normal distribution probability density function (PDF).
We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we’ve built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.
The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.
When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.
To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
[Truncated normal][truncated-normal-distribution] distribution probability density function (PDF).
X conditional on a < X < b is called a [truncated normal][truncated-normal-distribution] distribution.math
f(x;\mu,\sigma,a,b) = \begin{cases} \frac{\frac{1}{\sigma}\phi(\frac{x - \mu}{\sigma})}{\Phi(\frac{b - \mu}{\sigma}) - \Phi(\frac{a - \mu}{\sigma}) } & \text{ if } a < x < b \\ 0 & \text{ otherwise } \end{cases}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.bash
npm install @stdlib/stats-base-dists-truncated-normal-pdfscript tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).deno][deno-url] branch (see [README][deno-readme] for usage intructions).umd][umd-url] branch (see [README][umd-readme]).javascript
var pdf = require( '@stdlib/stats-base-dists-truncated-normal-pdf' );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 0.0NaN 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 NaNjavascript
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 ~0.996javascript
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, mu: %d, sigma: %d, f(x;a,b,mu,sigma): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), mu.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
}
