@stdlib/stats-base-dists-binomial-pmf
v0.3.1TypeScript
Binomial distribution probability mass function (PMF).
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Probability Mass Function
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> [Binomial][binomial-distribution] distribution probability mass function (PMF).
The [probability mass function][pmf] (PMF) for a [binomial][binomial-distribution] random variable is
where n is the number of trials and 0 <= p <= 1 is the success probability.
Installation
``bash`
npm install @stdlib/stats-base-dists-binomial-pmf
Usage
`javascript`
var pmf = require( '@stdlib/stats-base-dists-binomial-pmf' );
#### pmf( x, n, p )
Evaluates the [probability mass function][pmf] (PMF) for a [binomial][binomial-distribution] distribution with number of trials n and success probability p.
`javascript
var y = pmf( 3.0, 20, 0.2 );
// returns ~0.205
y = pmf( 21.0, 20, 0.2 );
// returns 0.0
y = pmf( 5.0, 10, 0.4 );
// returns ~0.201
y = pmf( 0.0, 10, 0.4 );
// returns ~0.006
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = pmf( NaN, 20, 0.5 );
// returns NaN
y = pmf( 0.0, NaN, 0.5 );
// returns NaN
y = pmf( 0.0, 20, NaN );
// returns NaN
`
If provided a number of trials n which is not a nonnegative integer, the function returns NaN.
`javascript
var y = pmf( 2.0, 1.5, 0.5 );
// returns NaN
y = pmf( 2.0, -2.0, 0.5 );
// returns NaN
`
If provided a success probability p outside of [0,1], the function returns NaN.
`javascript
var y = pmf( 2.0, 20, -1.0 );
// returns NaN
y = pmf( 2.0, 20, 1.5 );
// returns NaN
`
#### pmf.factory( n, p )
Returns a function for evaluating the [probability mass function][pmf] (PMF) of a [binomial][binomial-distribution] distribution with number of trials n and success probability p.
`javascript
var mypmf = pmf.factory( 10, 0.5 );
var y = mypmf( 3.0 );
// returns ~0.117
y = mypmf( 5.0 );
// returns ~0.246
`
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 pmf = require( '@stdlib/stats-base-dists-binomial-pmf' );
var opts = {
'dtype': 'float64'
};
var x = discreteUniform( 10, 0, 20, opts );
var n = discreteUniform( 10, 0, 100, opts );
var p = uniform( 10, 0.0, 1.0, opts );
logEachMap( 'x: %0.4f, n: %0.4f, p: %0.4f, P(X = x;n,p): %0.4f', x, n, p, pmf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/binomial/pmf.h"
#### stdlib_base_dists_binomial_pmf( x, n, p )
Evaluates the probability mass function (PMF) for a binomial distribution with number of trials n and success probability p at a value x.
`c`
double out = stdlib_base_dists_binomial_pmf( 3.0, 20, 0.2 );
// returns ~0.205
The function accepts the following arguments:
- x: [in] double input value.[in] int32_t
- n: number of trials.[in] double
- p: success probability.
`c`
double stdlib_base_dists_binomial_pmf( const double x, const int32_t n, const double p );
$3
`c
#include "stdlib/stats/base/dists/binomial/pmf.h"
#include
#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) );
}
static int32_t random_int( const int32_t min, const int32_t max ) {
return min + (int32_t)( random_uniform( 0.0, 1.0 ) * ( max - min + 1 ) );
}
int main( void ) {
int32_t n;
double p;
double x;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
n = random_int( 1, 20 );
x = random_uniform( 0.0, (double)n );
p = random_uniform( 0.0, 1.0 );
y = stdlib_base_dists_binomial_pmf( x, n, p );
printf( "x: %.4f, n: %d, p: %.4f, P(X = x;n,p): %.4f\n", x, n, p, 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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[binomial-distribution]: https://en.wikipedia.org/wiki/Binomial_distribution
[pmf]: https://en.wikipedia.org/wiki/Probability_mass_function