Planck (discrete exponential) distribution probability mass function (PMF).
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> Planck (discrete exponential) distribution [probability mass function][pmf] (PMF).
The [probability mass function][pmf] (PMF) for a Planck random variable is defined as
where λ is the shape parameter. The random variable X denotes the count of events in a quantized system.
``bash`
npm install @stdlib/stats-base-dists-planck-pmf
`javascript`
var pmf = require( '@stdlib/stats-base-dists-planck-pmf' );
#### pmf( x, lambda )
Evaluates the [probability mass function][pmf] (PMF) of a Planck (discrete exponential) distribution with shape parameter lambda.
`javascript
var y = pmf( 4.0, 0.3 );
// returns ~0.0781
y = pmf( 2.0, 1.7 );
// returns ~0.0273
y = pmf( -1.0, 2.5 );
// returns 0.0
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = pmf( NaN, 0.0 );
// returns NaN
y = pmf( 0.0, NaN );
// returns NaN
`
If provided a shape parameter lambda which is a nonpositive number, the function returns NaN.
`javascript`
var y = pmf( 2.0, -1.0 );
// returns NaN
#### pmf.factory( lambda )
Returns a function for evaluating the [probability mass function][pmf] (PMF) of a Planck (discrete exponential) distribution with shape parameter lambda.
`javascript
var mypmf = pmf.factory( 0.5 );
var y = mypmf( 3.0 );
// returns ~0.0878
y = mypmf( 1.0 );
// returns ~0.2387
`
`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-planck-pmf' );
var opts = {
'dtype': 'float64'
};
var x = discreteUniform( 10, 0, 5, opts );
var lambda = uniform( 10, 0.1, 5.0, opts );
logEachMap( 'x: %d, λ: %0.4f, P(X = x; λ): %0.4f', x, lambda, pmf );
`
*
`c`
#include "stdlib/stats/base/dists/planck/pmf.h"
#### stdlib_base_dists_planck_pmf( x, lambda )
Evaluates the [probability mass function][pmf] for a Planck (discrete exponential) distribution with input value x and shape parameter lambda.
`c`
double out = stdlib_base_dists_planck_pmf( 4.0, 0.3 );
// returns ~0.0781
The function accepts the following arguments:
- x: [in] double input value.[in] double
- lambda: shape parameter.
`c`
double stdlib_base_dists_planck_pmf( const double x, const double lambda );
`c
#include "stdlib/stats/base/dists/planck/pmf.h"
#include "stdlib/math/base/special/round.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 x;
double lambda;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
x = stdlib_base_round( random_uniform( 0.0, 11.0 ) );
lambda = random_uniform( 0.1, 5.0 );
y = stdlib_base_dists_planck_pmf( x, lambda );
printf( "x: %.0f, λ: %lf, P(X = x; λ): %lf\n", x, lambda, y );
}
}
`
*
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].
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[pmf]: https://en.wikipedia.org/wiki/Probability_mass_function