time-to-botec

Benchmark sampling in different programming languages
Log | Files | Refs | README

factory.js (2900B)

      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 constantFunction = require( '@stdlib/utils/constant-function' );
     24 var cdf = require( './../../../../../base/dists/negative-binomial/cdf' );
     25 var erfcinv = require( '@stdlib/math/base/special/erfcinv' );
     26 var isnan = require( '@stdlib/math/base/assert/is-nan' );
     27 var round = require( '@stdlib/math/base/special/round' );
     28 var sqrt = require( '@stdlib/math/base/special/sqrt' );
     29 var SQRT2 = require( '@stdlib/constants/float64/sqrt-two' );
     30 var PINF = require( '@stdlib/constants/float64/pinf' );
     31 var search = require( './search.js' );
     32 
     33 
     34 // MAIN //
     35 
     36 /**
     37 * Returns a function for evaluating the quantile function for a negative binomial distribution with number of successes until experiment is stopped `r` and success probability `p`.
     38 *
     39 * @param {PositiveNumber} r - number of successes until experiment is stopped
     40 * @param {Probability} p - success probability
     41 * @returns {Function} quantile function
     42 *
     43 * @example
     44 * var quantile = factory( 10.0, 0.5 );
     45 * var y = quantile( 0.1 );
     46 * // returns 5
     47 *
     48 * y = quantile( 0.9 );
     49 * // returns 16
     50 */
     51 function factory( r, p ) {
     52 	var sigmaInv;
     53 	var sigma;
     54 	var mu;
     55 	var q;
     56 	if (
     57 		isnan( r ) ||
     58 		isnan( p ) ||
     59 		r <= 0.0 ||
     60 		p < 0.0 ||
     61 		p > 1.0
     62 	) {
     63 		return constantFunction( NaN );
     64 	}
     65 	q = 1.0 - p;
     66 	mu = ( r * q ) / p;
     67 	sigma = sqrt( r * q ) / p;
     68 	sigmaInv = ( (2.0/p) - 1.0 ) / sigma;
     69 	return quantile;
     70 
     71 	/**
     72 	* Evaluates the quantile function for a negative binomial distribution.
     73 	*
     74 	* @private
     75 	* @param {Probability} k - input value
     76 	* @returns {NonNegativeInteger} evaluated quantile function
     77 	*
     78 	* @example
     79 	* var y = quantile( 0.3 );
     80 	* // returns <number>
     81 	*/
     82 	function quantile( k ) {
     83 		var guess;
     84 		var corr;
     85 		var x2;
     86 		var x;
     87 
     88 		if ( isnan( k ) || k < 0.0 || k > 1.0 ) {
     89 			return NaN;
     90 		}
     91 		if ( k === 0.0 ) {
     92 			return 0.0;
     93 		}
     94 		if ( k === 1.0 ) {
     95 			return PINF;
     96 		}
     97 
     98 		// Cornish-Fisher expansion:
     99 		if ( k < 0.5 ) {
    100 			x = -erfcinv( 2.0 * k ) * SQRT2;
    101 		} else {
    102 			x = erfcinv( 2.0 * (1.0-k) ) * SQRT2;
    103 		}
    104 		x2 = x * x;
    105 
    106 		// Skewness correction:
    107 		corr = x + (sigmaInv * ( x2 - 1.0 ) / 6.0);
    108 		guess = round( mu + (sigma * corr) );
    109 		return ( cdf( guess, r, p ) >= k ) ?
    110 			search.left( guess, k, r, p ) :
    111 			search.right( guess, k, r, p );
    112 	}
    113 }
    114 
    115 
    116 // EXPORTS //
    117 
    118 module.exports = factory;