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

0.2.1 • Public • Published

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# Logarithm of Probability Density Function

Logistic distribution logarithm of probability density function (PDF).

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

where `mu` is the location parameter and `s` is the scale parameter.

## Installation

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

## Usage

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

#### logpdf( x, mu, s )

Evaluates the logarithm of the probability density function (PDF) for a logistic distribution with parameters `mu` (location parameter) and `s` (scale parameter).

```var y = logpdf( 2.0, 0.0, 1.0 );
// returns ~-2.254

y = logpdf( -1.0, 4.0, 4.0 );
// returns ~-3.14```

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 `s < 0`, the function returns `NaN`.

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

If provided `s = 0`, the function evaluates the 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, s )

Returns a function for evaluating the logarithm of the probability density function (PDF) of a logistic distribution with parameters `mu` (location parameter) and `s` (scale parameter).

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

var y = mylogpdf( 10.0 );
// returns ~-2.079

y = mylogpdf( 5.0 );
// returns ~-3.351```

## Notes

• In virtually all cases, using the `logpdf` or `logcdf` functions is preferable to manually computing the logarithm of the `pdf` or `cdf`, respectively, since the latter is prone to overflow and underflow.

## Examples

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

var mu;
var s;
var x;
var y;
var i;

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

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