@stdlib/stats-base-dists-poisson-logpmf
v0.3.1TypeScript
Natural logarithm of the probability mass function (PMF) for a Poisson distribution.
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Published by The Stdlib Authors
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About stdlib...
Logarithm of Probability Mass Function
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> Evaluate the natural logarithm of the [probability mass function][pmf] (PMF) for a [Poisson][poisson-distribution] distribution.
The [probability mass function][pmf] (PMF) for a [Poisson][poisson-distribution] random variable is
where lambda > 0 is the mean parameter.
Installation
``bash`
npm install @stdlib/stats-base-dists-poisson-logpmf
Usage
`javascript`
var logpmf = require( '@stdlib/stats-base-dists-poisson-logpmf' );
#### logpmf( x, lambda )
Evaluates the natural logarithm of the [probability mass function][pmf] (PMF) for a [Poisson][poisson-distribution] distribution with mean parameter lambda.
`javascript
var y = logpmf( 4.0, 3.0 );
// returns ~-1.784
y = logpmf( 1.0, 3.0 );
// returns ~-1.901
y = logpmf( -1.0, 2.0 );
// returns -Infinity
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = logpmf( NaN, 2.0 );
// returns NaN
y = logpmf( 0.0, NaN );
// returns NaN
`
If provided a negative mean parameter lambda, the function returns NaN.
`javascript
var y = logpmf( 2.0, -1.0 );
// returns NaN
y = logpmf( 4.0, -2.0 );
// returns NaN
`
If provided lambda = 0, the function evaluates the natural logarithm of the [PMF][pmf] of a [degenerate distribution][degenerate-distribution] centered at 0.0.
`javascript
var y = logpmf( 2.0, 0.0 );
// returns -Infinity
y = logpmf( 0.0, 0.0 );
// returns 0.0
`
#### logpmf.factory( lambda )
Returns a function for evaluating the natural logarithm of the [probability mass function][pmf] (PMF) for a [Poisson][poisson-distribution] distribution with mean parameter lambda.
`javascript
var mylogpmf = logpmf.factory( 1.0 );
var y = mylogpmf( 3.0 );
// returns ~-2.792
y = mylogpmf( 1.0 );
// returns ~-1.0
`
Examples
`javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var logpmf = require( '@stdlib/stats-base-dists-poisson-logpmf' );
var opts = {
'dtype': 'float64'
};
var x = discreteUniform( 10, 0.0, 10.0, opts );
var lambda = uniform( 10, 0.0, 10.0, opts );
logEachMap( 'x: %d, λ: %0.4f, ln(P(X=x;λ)): %0.4f', x, lambda, logpmf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/poisson/logpmf.h"
#### stdlib_base_dists_poisson_logpmf( x, lambda )
Evaluates the natural logarithm of the [probability mass function][pmf] (PMF) for a [Poisson][poisson-distribution] distribution with mean parameter lambda.
`c`
double out = stdlib_base_dists_poisson_logpmf( 4.0, 3.0 );
// returns ~-1.784
The function accepts the following arguments:
- x: [in] double input value.[in] double
- lambda: mean parameter.
`c`
double stdlib_base_dists_poisson_logpmf( const double x, const double lambda );
$3
`c
#include "stdlib/stats/base/dists/poisson/logpmf.h"
#include "stdlib/random/base/ceil.h"
#include
#include
static double random_uniform( const double min, const double max ) {
double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
return min + ( v*(max-min) );
}
int main( void ) {
double lambda;
double x;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
x = stdlib_base_ceil( random_uniform( 0.0, 10.0 ) );
lambda = random_uniform( 0.0, 10.0);
y = stdlib_base_dists_poisson_logpmf( x, lambda );
printf( "x: %lf, λ: %lf, ln(P(X=x;λ)): %lf\n", x, lambda, y );
}
}
`
*
Notice
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
[poisson-distribution]: https://en.wikipedia.org/wiki/Poisson_distribution
[pmf]: https://en.wikipedia.org/wiki/Probability_mass_function