@stdlib/stats-base-dists-gamma-logcdf
v0.3.1TypeScript
Gamma distribution logarithm of cumulative distribution function (CDF).
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About stdlib...
Logarithm of Cumulative Distribution Function
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> [Gamma][gamma-distribution] distribution logarithm of cumulative distribution function (CDF).
The [cumulative distribution function][cdf] for a [gamma][gamma-distribution] random variable is
where alpha is the shape parameter and beta is the rate parameter of the distribution. gamma is the lower [incomplete gamma function][@stdlib/math/base/special/gammainc].
Installation
``bash`
npm install @stdlib/stats-base-dists-gamma-logcdf
Usage
`javascript`
var logcdf = require( '@stdlib/stats-base-dists-gamma-logcdf' );
#### logcdf( x, alpha, beta )
Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF) for a [gamma][gamma-distribution] distribution with parameters alpha (shape parameter) and beta (rate parameter).
`javascript
var y = logcdf( 2.0, 0.5, 1.0 );
// returns ~-0.047
y = logcdf( 0.1, 1.0, 1.0 );
// returns ~-2.352
y = logcdf( -1.0, 4.0, 2.0 );
// returns -Infinity
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = logcdf( NaN, 1.0, 1.0 );
// returns NaN
y = logcdf( 0.0, NaN, 1.0 );
// returns NaN
y = logcdf( 0.0, 1.0, NaN );
// returns NaN
`
If provided alpha < 0, the function returns NaN.
`javascript`
var y = logcdf( 2.0, -0.5, 1.0 );
// returns NaN
If provided alpha = 0, the function evaluates the logarithm of the [CDF][cdf] for a [degenerate distribution][degenerate-distribution] centered at 0.
`javascript
var y = logcdf( 2.0, 0.0, 2.0 );
// returns 0.0
y = logcdf( -2.0, 0.0, 2.0 );
// returns -Infinity
y = logcdf( 0.0, 0.0, 2.0 );
// returns 0.0
`
If provided beta <= 0, the function returns NaN.
`javascript
var y = logcdf( 2.0, 1.0, 0.0 );
// returns NaN
y = logcdf( 2.0, 1.0, -1.0 );
// returns NaN
`
#### logcdf.factory( alpha, beta )
Returns a function for evaluating the natural logarithm of the [CDF][cdf] for a [gamma][gamma-distribution] distribution with parameters alpha (shape parameter) and beta (rate parameter).
`javascript
var mylogcdf = logcdf.factory( 3.0, 1.5 );
var y = mylogcdf( 1.0 );
// returns ~-1.655
y = mylogcdf( 4.0 );
// returns ~-0.064
`
*
$3
#### Usage
`c`
#include "stdlib/stats/base/dists/gamma/logcdf.h"
#### stdlib_base_dists_gamma_logcdf( x, alpha, beta )
Evaluates the natural logarithm of the cumulative distribution function (CDF) for a gamma distribution with shape parameter alpha and rate parameter beta.
`c
double out = stdlib_base_dists_gamma_logcdf( 2.0, 0.5, 1.0 );
// returns ~-0.047
out = stdlib_base_dists_gamma_logcdf( 0.1, 1.0, 1.0 );
// returns ~-2.352
`
The function accepts the following arguments:
- x: [in] double input value.[in] double
- alpha: shape parameter.[in] double
- beta: rate parameter.
`c`
double stdlib_base_dists_gamma_logcdf( const double x, const double alpha, const double beta );
$3
`c
#include "stdlib/stats/base/dists/gamma/logcdf.h"
#include
#include
static double random_uniform( double a, double b ) {
double r = ( (double)rand() / ( (double)RAND_MAX + 1.0 ) );
return a + ( r * ( b - a ) );
}
int main( void ) {
double alpha;
double beta;
double x;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
x = random_uniform( 0.0, 2.0 );
alpha = random_uniform( 1.0, 10.0 );
beta = random_uniform( 1.0, 10.0 );
y = stdlib_base_dists_gamma_logcdf( x, alpha, beta );
printf( "x: %lf, α: %lf, β: %lf, ln(F(x;α,β)): %lf\n", x, alpha, beta, y );
}
}
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var logcdf = require( '@stdlib/stats-base-dists-gamma-logcdf' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 10, 0.0, 3.0, opts );
var alpha = uniform( 10, 0.0, 5.0, opts );
var beta = uniform( 10, 0.0, 5.0, opts );
logEachMap( 'x: %0.4f, α: %0.4f, β: %0.4f, ln(f(x;α,β)): %0.4f', x, alpha, beta, logcdf );
`
*
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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[deno-readme]: https://github.com/stdlib-js/stats-base-dists-gamma-logcdf/blob/deno/README.md
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-gamma-logcdf/main/LICENSE
[gamma-distribution]: https://en.wikipedia.org/wiki/Gamma_distribution
[cdf]: https://en.wikipedia.org/wiki/Cumulative_Distribution_Function
[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
[@stdlib/math/base/special/gammainc]: https://www.npmjs.com/package/@stdlib/math-base-special-gammainc