72 lines
2.1 KiB
JavaScript
72 lines
2.1 KiB
JavaScript
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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2018 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var factorial = require( '@stdlib/math/base/special/factorial' );
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// MAIN //
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/**
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* Returns a pseudorandom number drawn from a hypergeometric distribution using the HIN algorithm, which is based on an inverse transformation method.
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*
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* ## References
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*
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* - Fishman, George S. 1973. _Concepts and methods in discrete event digital simulation_. A Wiley-Interscience Publication. New York, NY, USA: Wiley.
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* - 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].
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*
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* [@kachitvichyanukul:1985]: http://dx.doi.org/10.1080/00949658508810839
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*
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*
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* @private
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* @param {PRNG} rand - PRNG for uniformly distributed numbers
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* @param {NonNegativeInteger} n1 - number of successes in population
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* @param {NonNegativeInteger} n2 - number of failures in population
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* @param {NonNegativeInteger} k - number of draws
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* @returns {NonNegativeInteger} pseudorandom number
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*/
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function hin( rand, n1, n2, k ) {
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var p;
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var u;
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var x;
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if ( k < n2 ) {
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p = ( factorial( n2 ) * factorial( n1 + n2 - k ) ) /
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( factorial( n1 + n2 ) * factorial( n2 - k ) );
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x = 0;
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} else {
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p = ( factorial( n1 ) * factorial( k ) ) /
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( factorial( k - n2 ) * factorial( n1 + n2 ) );
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x = k - n2;
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}
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u = rand();
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while ( u > p ) {
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u -= p;
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p *= ( n1 - x ) * ( k - x ) / ( ( x + 1 ) * ( n2 - k + 1 + x ) );
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x += 1;
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}
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return x;
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}
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// EXPORTS //
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module.exports = hin;
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