@stdlib/stats-base-dists-truncated-normal-pdf
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Truncated normal distribution probability density function (PDF).
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Probability Density Function
Truncated normal distribution probability density function (PDF).
A normally distributed random variable X
conditional on a < X < b
is called a truncated normal distribution.
The probability density function (PDF) for a truncated normal random variable is
where Phi
and phi
denote the cumulative distribution function and density function of the normal 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
npm install @stdlib/stats-base-dists-truncated-normal-pdf
Usage
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 distribution with lower limit a
, upper limit b
, location parameter mu
, and scale parameter sigma
.
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
.
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) for a truncated normal distribution.
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
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 ) );
}
Notice
This package is part of 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, see the main project repository.
Community
License
See LICENSE.
Copyright
Copyright © 2016-2024. The Stdlib Authors.