Ninety Percent Muffin

# npm

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

0.0.7 • Public • Published

# Logarithm of Probability Density Function

Evaluate the natural logarithm of the probability density function (PDF) for an Erlang distribution.

The probability density function (PDF) for an Erlang random variable is

where `k` is the shape parameter and `lambda` is the rate parameter.

## Installation

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

## Usage

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

#### logpdf( x, k, lambda )

Evaluates the natural logarithm of the probability density function (PDF) for an Erlang distribution with parameters `k` (shape parameter) and `lambda` (rate parameter).

```var y = logpdf( 0.1, 1, 1.0 );
// returns ~-0.1

y = logpdf( 0.5, 2, 2.5 );
// returns ~-0.111

y = logpdf( -1.0, 4, 2.0 );
// returns -Infinity```

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

```var y = logpdf( NaN, 1, 1.0 );
// returns NaN

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

y = logpdf( 0.0, 1, NaN );
// returns NaN```

If not provided a nonnegative integer for `k`, the function returns `NaN`.

```var y = logpdf( 2.0, -2, 0.5 );
// returns NaN

y = logpdf( 2.0, 0.5, 0.5 );
// returns NaN```

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

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

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

If provided `lambda <= 0`, the function returns `NaN`.

```var y = logpdf( 2.0, 1, 0.0 );
// returns NaN

y = logpdf( 2.0, 1, -1.0 );
// returns NaN```

#### logpdf.factory( k, lambda )

Returns a `function` for evaluating the PDF for an Erlang distribution with parameters `k` (shape parameter) and `lambda` (rate parameter).

```var mylogpdf = logpdf.factory( 3, 1.5 );

var y = mylogpdf( 1.0 );
// returns ~-0.977

y = mylogpdf( 4.0 );
// returns ~-2.704```

## Examples

```var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var logpdf = require( '@stdlib/stats-base-dists-erlang-logpdf' );

var lambda;
var k;
var x;
var y;
var i;

for ( i = 0; i < 20; i++ ) {
x = randu() * 10.0;
k = round( randu() * 10.0 );
lambda = randu() * 5.0;
y = logpdf( x, k, lambda );
console.log( 'x: %d, k: %d, λ: %d, ln(f(x;k,λ)): %d', x.toFixed( 4 ), k, lambda.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.

### Install

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

stdlib.io

77

0.0.7

Apache-2.0

42.9 kB

11