Inverse gamma distribution cumulative distribution function (CDF).
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[Inverse Gamma][inverse-gamma] distribution [cumulative distribution function][cdf].
math
F(x; \alpha, \beta) = \frac{\Gamma\left(\alpha,\frac{\beta}{x}\right)}{\Gamma(\alpha)} = Q\left(\frac{\beta}{x},\alpha\right)alpha > 0 is the shape parameter and beta > 0 is the scale parameter. Q is the upper regularized incomplete gamma function.bash
npm install @stdlib/stats-base-dists-invgamma-cdfscript tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).deno][deno-url] branch (see [README][deno-readme] for usage intructions).umd][umd-url] branch (see [README][umd-readme]).javascript
var cdf = require( '@stdlib/stats-base-dists-invgamma-cdf' );alpha (shape parameter) and beta (rate parameter).javascript
var y = cdf( 2.0, 1.0, 1.0 );
// returns ~0.607
y = cdf( 2.0, 3.0, 1.0 );
// returns ~0.986
y = cdf( -1.0, 2.0, 2.0 );
// returns 0.0
y = cdf( -Infinity, 4.0, 2.0 );
// returns 0.0
y = cdf( +Infinity, 4.0, 2.0 );
// returns 1.0NaN as any argument, the function returns NaN.javascript
var y = cdf( NaN, 1.0, 1.0 );
// returns NaN
y = cdf( 0.0, NaN, 1.0 );
// returns NaN
y = cdf( 0.0, 1.0, NaN );
// returns NaNalpha <= 0, the function returns NaN.javascript
var y = cdf( 2.0, -1.0, 0.5 );
// returns NaNbeta <= 0, the function returns NaN.javascript
var y = cdf( 2.0, 0.5, -1.0 );
// returns NaNalpha (shape parameter) and beta (rate parameter).javascript
var mycdf = cdf.factory( 0.5, 0.1 );
var y = mycdf( 12.0 );
// returns ~0.897
y = mycdf( 8.0 );
// returns ~0.874c
#include "stdlib/stats/base/dists/invgamma/cdf.h"alpha (shape parameter) and beta (scale parameter).c
double out = stdlib_base_dists_invgamma_cdf( 2.0, 1.0, 1.0 );
// returns ~0.607
out = stdlib_base_dists_invgamma_cdf( 2.0, 3.0, 1.0 );
// returns ~0.986[in] double input value.[in] double shape parameter.[in] double scale parameter.c
double stdlib_base_dists_invgamma_cdf( const double x, const double alpha, const double beta );c
#include "stdlib/stats/base/dists/invgamma/cdf.h"
#include <stdlib.h>
#include <stdio.h>
static double random_uniform( double min, double max ) {
double scale = rand() / (double) RAND_MAX;
return min + ( scale * ( max - min ) );
}
int main( void ) {
double alpha;
double beta;
double x;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
x = random_uniform( 0.1, 5.0 );
alpha = random_uniform( 1.0, 5.0 );
beta = random_uniform( 1.0, 5.0 );
y = stdlib_base_dists_invgamma_cdf( x, alpha, beta );
printf( "x: %lf, α: %lf, β: %lf, F(x;α,β): %lf\n", x, alpha, beta, y );
}
}javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var cdf = require( '@stdlib/stats-base-dists-invgamma-cdf' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 10, 0.0, 2.0, 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, F(x;α,β): %0.4f', x, alpha, beta, cdf );
