time-to-botec/js/node_modules/@stdlib/random/base/poisson/lib/rejection.js
NunoSempere b6addc7f05 feat: add the node modules
Necessary in order to clearly see the squiggle hotwiring.
2022-12-03 12:44:49 +00:00

123 lines
2.8 KiB
JavaScript
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

/**
* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MODULES //
var factorialln = require( '@stdlib/math/base/special/factorialln' );
var floor = require( '@stdlib/math/base/special/floor' );
var sign = require( '@stdlib/math/base/special/signum' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var abs = require( '@stdlib/math/base/special/abs' );
var ln = require( '@stdlib/math/base/special/ln' );
var LN_SQRT_TWO_PI = require( '@stdlib/constants/float64/ln-sqrt-two-pi' );
// VARIABLES //
var ONE_12 = 1.0 / 12.0;
var ONE_360 = 1.0 / 360.0;
// MAIN //
/**
* Returns a pseudorandom number drawn from a Poisson distribution with parameter `lambda`.
*
* ## References
*
* - Hörmann, W. 1993. "The transformed rejection method for generating Poisson random variables." _Insurance: Mathematics and Economics_ 12 (1): 3945. doi:[10.1016/0167-6687(93)90997-4][@hormann:1993b].
*
* [@hormann:1993b]: http://dx.doi.org/10.1016/0167-6687(93)90997-4
*
*
* @private
* @param {PRNG} rand - PRNG for generating uniformly distributed numbers
* @param {PositiveNumber} lambda - mean
* @returns {NonNegativeInteger} pseudorandom number
*/
function poisson( rand, lambda ) {
var slambda;
var ainv;
var urvr;
var us;
var vr;
var a;
var b;
var k;
var u;
var v;
slambda = sqrt( lambda );
b = (2.53*slambda) + 0.931;
a = (0.02483*b) - 0.059;
ainv = (1.1328/(b-3.4)) + 1.1239;
vr = (-3.6224/(b-2.0)) + 0.9277;
urvr = 0.86 * vr;
while ( true ) {
v = rand();
if ( v <= urvr ) {
u = (v / vr) - 0.43;
u *= (2.0*a / (0.5-abs(u))) + b;
u += lambda + 0.445;
return floor( u );
}
if ( v >= vr ) {
u = rand() - 0.5;
} else {
u = (v / vr) - 0.93;
u = (sign( u )*0.5) - u;
v = vr * rand();
}
us = 0.5 - abs( u );
if (
us >= 0.013 ||
us >= v
) {
k = floor( (((2.0*a/us) + b)*u) + lambda + 0.445 );
v *= ainv / ( (a/(us*us)) + b );
u = (k+0.5) * ln( lambda/k );
u += -lambda - LN_SQRT_TWO_PI + k;
u -= ( ONE_12 - (ONE_360/(k*k)) ) / k;
if (
k >= 10 &&
u >= ln( v*slambda )
) {
return k;
}
u = (k*ln( lambda )) - lambda - factorialln( k );
if (
k >= 0 &&
k <= 9 &&
u >= ln( v )
) {
return k;
}
}
}
}
// EXPORTS //
module.exports = poisson;