gammainc
Evaluates the regularized lower incomplete gamma function:
The function can also be used to evaluate the regularized upper incomplete gamma function, which is defined as follows:
The two functions have the relationship Q(x,a) = 1 - P(x,a).
In addition, this routine can be used to evaluate the unregularized gamma functions. The range of above functions is [0,1], which is not the case for the unregularized versions. The unregularized lower incomplete gamma function is defined as
and the upper unregularized incomplete gamma function is
The relationship between the two functions is Γ(a,x) = γ(a,x) + Γ(a).
Usage
var gammainc = require( '@stdlib/math/base/special/gammainc' );
gammainc( x, s[, regularized[, upper ]] )
By default, evaluates the regularized lower incomplete gamma function for inputs x and s. The third and fourth parameters of the function can be used to specify whether instead to evaluate the non-regularized and/or upper incomplete gamma functions, respectively.
var y = gammainc( 6.0, 2.0 );
// returns ~0.9826
y = gammainc( 1.0, 2.0, true, true );
// returns ~0.7358
y = gammainc( 7.0, 5.0 );
// returns ~0.8270
y = gammainc( 7.0, 5.0, false );
// returns ~19.8482
If provided NaN as any argument, the function returns NaN.
var y = gammainc( NaN, 1.0 );
// returns NaN
y = gammainc( 1.0, NaN );
// returns NaN
If provided a negative x, the function returns NaN.
var y = gammainc( -2.0, 2.0 );
// returns NaN
If provided a nonpositive s, the function returns NaN.
var y = gammainc( 2.0, -1.0 );
// returns NaN
y = gammainc( 2.0, 0.0 );
// returns NaN
Examples
var randu = require( '@stdlib/random/base/randu' );
var gammainc = require( '@stdlib/math/base/special/gammainc' );
var i;
var x;
var s;
for ( i = 0; i < 100; i++ ) {
x = randu() * 10.0;
s = randu() * 10.0;
console.log( 'x: %d, \t s: %d, \t f(x,s): %d', x.toFixed( 4 ), s.toFixed( 4 ), gammainc( x, s ).toFixed( 4 ) );
}