time-to-botec

Benchmark sampling in different programming languages
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quantile.js (2633B)

      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 erfcinv = require( '@stdlib/math/base/special/erfcinv' );
     24 var isnan = require( '@stdlib/math/base/assert/is-nan' );
     25 var round = require( '@stdlib/math/base/special/round' );
     26 var sqrt = require( '@stdlib/math/base/special/sqrt' );
     27 var cdf = require( './../../../../../base/dists/poisson/cdf' );
     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 Poisson distribution with mean parameter `lambda` at a probability `p`.
     37 *
     38 * @param {Probability} p - input value
     39 * @param {NonNegativeNumber} lambda - mean parameter
     40 * @returns {NonNegativeInteger} evaluated quantile function
     41 *
     42 * @example
     43 * var y = quantile( 0.5, 2.0 );
     44 * // returns 2
     45 *
     46 * @example
     47 * var y = quantile( 0.9, 4.0 );
     48 * // returns 7
     49 *
     50 * @example
     51 * var y = quantile( 0.1, 200.0 );
     52 * // returns 182
     53 *
     54 * @example
     55 * var y = quantile( 1.1, 0.0 );
     56 * // returns NaN
     57 *
     58 * @example
     59 * var y = quantile( -0.2, 0.0 );
     60 * // returns NaN
     61 *
     62 * @example
     63 * var y = quantile( NaN, 0.5 );
     64 * // returns NaN
     65 *
     66 * @example
     67 * var y = quantile( 0.0, NaN );
     68 * // returns NaN
     69 */
     70 function quantile( p, lambda ) {
     71 	var sigmaInv;
     72 	var guess;
     73 	var sigma;
     74 	var corr;
     75 	var x2;
     76 	var x;
     77 	if ( isnan( lambda ) || lambda < 0.0 ) {
     78 		return NaN;
     79 	}
     80 	if ( isnan( p ) || p < 0.0 || p > 1.0 ) {
     81 		return NaN;
     82 	}
     83 	if ( lambda === 0.0 ) {
     84 		return 0.0;
     85 	}
     86 	if ( p === 0.0 ) {
     87 		return 0.0;
     88 	}
     89 	if ( p === 1.0 ) {
     90 		return PINF;
     91 	}
     92 	// Cornish-Fisher expansion:
     93 	sigma = sqrt( lambda );
     94 	sigmaInv = 1.0 / sigma;
     95 	if ( p < 0.5 ) {
     96 		x = -erfcinv( 2.0 * p ) * SQRT2;
     97 	} else {
     98 		x = erfcinv( 2.0 * ( 1.0 - p ) ) * SQRT2;
     99 	}
    100 	x2 = x * x;
    101 
    102 	// Skewness correction:
    103 	corr = x + (sigmaInv * ( x2 - 1.0 ) / 6.0);
    104 	guess = round( lambda + (sigma * corr) );
    105 	return ( cdf( guess, lambda ) >= p ) ?
    106 		search.left( guess, p, lambda ) :
    107 		search.right( guess, p, lambda );
    108 }
    109 
    110 
    111 // EXPORTS //
    112 
    113 module.exports = quantile;