time-to-botec

Benchmark sampling in different programming languages
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quantile.js (3246B)

      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 cdf = require( './../../../../../base/dists/negative-binomial/cdf' );
     24 var erfcinv = require( '@stdlib/math/base/special/erfcinv' );
     25 var isnan = require( '@stdlib/math/base/assert/is-nan' );
     26 var round = require( '@stdlib/math/base/special/round' );
     27 var sqrt = require( '@stdlib/math/base/special/sqrt' );
     28 var SQRT2 = require( '@stdlib/constants/float64/sqrt-two' );
     29 var PINF = require( '@stdlib/constants/float64/pinf' );
     30 var search = require( './search.js' );
     31 
     32 
     33 // MAIN //
     34 
     35 /**
     36 * Evaluates the quantile function for a negative binomial distribution with number of successes until experiment is stopped `r` and success probability `p` at a probability `k`.
     37 *
     38 * @param {Probability} k - input value
     39 * @param {PositiveNumber} r - number of successes until experiment is stopped
     40 * @param {Probability} p - success probability
     41 * @returns {NonNegativeInteger} evaluated quantile function
     42 *
     43 * @example
     44 * var y = quantile( 0.9, 20.0, 0.2 );
     45 * // returns 106
     46 *
     47 * @example
     48 * var y = quantile( 0.9, 20.0, 0.8 );
     49 * // returns 8
     50 *
     51 * @example
     52 * var y = quantile( 0.5, 10.0, 0.4 );
     53 * // returns 14
     54 *
     55 * @example
     56 * var y = quantile( 0.0, 10.0, 0.9 );
     57 * // returns 0
     58 *
     59 * @example
     60 * var y = quantile( 1.1, 20.0, 0.5 );
     61 * // returns NaN
     62 *
     63 * @example
     64 * var y = quantile( -0.1, 20.0, 0.5 );
     65 * // returns NaN
     66 *
     67 * @example
     68 * var y = quantile( 0.5, 0.0, 0.5 );
     69 * // returns NaN
     70 *
     71 * @example
     72 * var y = quantile( 0.5, -2.0, 0.5 );
     73 * // returns NaN
     74 *
     75 * @example
     76 * var y = quantile( 0.3, 20.0, -1.0 );
     77 * // returns NaN
     78 *
     79 * @example
     80 * var y = quantile( 0.3, 20.0, 1.5 );
     81 * // returns NaN
     82 *
     83 * @example
     84 * var y = quantile( NaN, 20.0, 0.5 );
     85 * // returns NaN
     86 *
     87 * @example
     88 * var y = quantile( 0.3, NaN, 0.5 );
     89 * // returns NaN
     90 *
     91 * @example
     92 * var y = quantile( 0.3, 20.0, NaN );
     93 * // returns NaN
     94 */
     95 function quantile( k, r, p ) {
     96 	var sigmaInv;
     97 	var guess;
     98 	var sigma;
     99 	var corr;
    100 	var mu;
    101 	var x2;
    102 	var x;
    103 	var q;
    104 
    105 	if (
    106 		isnan( r ) ||
    107 		isnan( p ) ||
    108 		isnan( k ) ||
    109 		r <= 0.0 ||
    110 		p < 0.0 ||
    111 		p > 1.0 ||
    112 		k < 0.0 ||
    113 		k > 1.0
    114 	) {
    115 		return NaN;
    116 	}
    117 	if ( k === 0.0 ) {
    118 		return 0.0;
    119 	}
    120 	if ( k === 1.0 ) {
    121 		return PINF;
    122 	}
    123 	q = 1.0 - p;
    124 	mu = ( r * q ) / p;
    125 	sigma = sqrt( r * q ) / p;
    126 	sigmaInv = 1.0 / sigma;
    127 
    128 	// Cornish-Fisher expansion:
    129 	if ( k < 0.5 ) {
    130 		x = -erfcinv( 2.0 * k ) * SQRT2;
    131 	} else {
    132 		x = erfcinv( 2.0 * (1.0-k) ) * SQRT2;
    133 	}
    134 	x2 = x * x;
    135 
    136 	// Skewness correction:
    137 	corr = x + (sigmaInv * ( x2 - 1.0 ) / 6.0);
    138 	guess = round( mu + (sigma * corr) );
    139 	return ( cdf( guess, r, p ) >= k ) ?
    140 		search.left( guess, k, r, p ) :
    141 		search.right( guess, k, r, p );
    142 }
    143 
    144 
    145 // EXPORTS //
    146 
    147 module.exports = quantile;