# @stdlib/stats-base-dists-normal-logpdf

0.2.1 • Public • Published

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# Logarithm of Probability Density Function

Evaluate the natural logarithm of the probability density function (PDF) for a normal distribution.

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

where `µ` is the mean and `σ` is the standard deviation.

## Installation

`npm install @stdlib/stats-base-dists-normal-logpdf`

## Usage

`var logpdf = require( '@stdlib/stats-base-dists-normal-logpdf' );`

#### logpdf( x, mu, sigma )

Evaluates the natural logarithm of the probability density function (PDF) for a normal distribution with parameters `mu` (mean) and `sigma` (standard deviation).

```var y = logpdf( 2.0, 0.0, 1.0 );
// returns ~-2.919

y = logpdf( -1.0, 4.0, 2.0 );
// returns ~-4.737```

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

```var y = logpdf( NaN, 0.0, 1.0 );
// returns NaN

y = logpdf( 0.0, NaN, 1.0 );
// returns NaN

y = logpdf( 0.0, 0.0, NaN );
// returns NaN```

If provided `sigma < 0`, the function returns `NaN`.

```var y = logpdf( 2.0, 0.0, -1.0 );
// returns NaN```

If provided `sigma = 0`, the function evaluates the natural logarithm of the PDF of a degenerate distribution centered at `mu`.

```var y = logpdf( 2.0, 8.0, 0.0 );
// returns -Infinity

y = logpdf( 8.0, 8.0, 0.0 );
// returns Infinity```

#### logpdf.factory( mu, sigma )

Returns a `function` for evaluating the probability density function (PDF) of a normal distribution with parameters `mu` (mean) and `sigma` (standard deviation).

```var mylogpdf = logpdf.factory( 10.0, 2.0 );

var y = mylogpdf( 10.0 );
// returns ~-1.612

y = mylogpdf( 5.0 );
// returns ~-4.737```

## Examples

```var randu = require( '@stdlib/random-base-randu' );
var logpdf = require( '@stdlib/stats-base-dists-normal-logpdf' );

var sigma;
var mu;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
x = randu() * 10.0;
mu = (randu() * 10.0) - 5.0;
sigma = randu() * 20.0;
y = logpdf( x, mu, sigma );
console.log( 'x: %d, µ: %d, σ: %d, ln(f(x;µ,σ)): %d', x, mu, sigma, y );
}```

## 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.

## Package Sidebar

### Install

`npm i @stdlib/stats-base-dists-normal-logpdf`

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