hin.js (2183B)
1 /** 2 * @license Apache-2.0 3 * 4 * Copyright (c) 2018 The Stdlib Authors. 5 * 6 * Licensed under the Apache License, Version 2.0 (the "License"); 7 * you may not use this file except in compliance with the License. 8 * You may obtain a copy of the License at 9 * 10 * http://www.apache.org/licenses/LICENSE-2.0 11 * 12 * Unless required by applicable law or agreed to in writing, software 13 * distributed under the License is distributed on an "AS IS" BASIS, 14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 15 * See the License for the specific language governing permissions and 16 * limitations under the License. 17 */ 18 19 'use strict'; 20 21 // MODULES // 22 23 var factorial = require( '@stdlib/math/base/special/factorial' ); 24 25 26 // MAIN // 27 28 /** 29 * Returns a pseudorandom number drawn from a hypergeometric distribution using the HIN algorithm, which is based on an inverse transformation method. 30 * 31 * ## References 32 * 33 * - Fishman, George S. 1973. _Concepts and methods in discrete event digital simulation_. A Wiley-Interscience Publication. New York, NY, USA: Wiley. 34 * - Kachitvichyanukul, Voratas., and Burce Schmeiser. 1985. "Computer generation of hypergeometric random variates." _Journal of Statistical Computation and Simulation_ 22 (2): 127–45. doi:[10.1080/00949658508810839][@kachitvichyanukul:1985]. 35 * 36 * [@kachitvichyanukul:1985]: http://dx.doi.org/10.1080/00949658508810839 37 * 38 * 39 * @private 40 * @param {PRNG} rand - PRNG for uniformly distributed numbers 41 * @param {NonNegativeInteger} n1 - number of successes in population 42 * @param {NonNegativeInteger} n2 - number of failures in population 43 * @param {NonNegativeInteger} k - number of draws 44 * @returns {NonNegativeInteger} pseudorandom number 45 */ 46 function hin( rand, n1, n2, k ) { 47 var p; 48 var u; 49 var x; 50 if ( k < n2 ) { 51 p = ( factorial( n2 ) * factorial( n1 + n2 - k ) ) / 52 ( factorial( n1 + n2 ) * factorial( n2 - k ) ); 53 x = 0; 54 } else { 55 p = ( factorial( n1 ) * factorial( k ) ) / 56 ( factorial( k - n2 ) * factorial( n1 + n2 ) ); 57 x = k - n2; 58 } 59 u = rand(); 60 while ( u > p ) { 61 u -= p; 62 p *= ( n1 - x ) * ( k - x ) / ( ( x + 1 ) * ( n2 - k + 1 + x ) ); 63 x += 1; 64 } 65 return x; 66 } 67 68 69 // EXPORTS // 70 71 module.exports = hin;