time-to-botec

Benchmark sampling in different programming languages
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cdf.js (2485B)

      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 betainc = require( '@stdlib/math/base/special/betainc' );
     24 var isnan = require( '@stdlib/math/base/assert/is-nan' );
     25 var floor = require( '@stdlib/math/base/special/floor' );
     26 var PINF = require( '@stdlib/constants/float64/pinf' );
     27 
     28 
     29 // MAIN //
     30 
     31 /**
     32 * Evaluates the cumulative distribution function (CDF) for a negative binomial distribution with number of successes until experiment is stopped `r` and success probability `p` at a value `x`.
     33 *
     34 * @param {number} x - input value
     35 * @param {PositiveNumber} r - number of successes until experiment is stopped
     36 * @param {Probability} p - success probability
     37 * @returns {Probability} evaluated CDF
     38 *
     39 * @example
     40 * var y = cdf( 5.0, 20.0, 0.8 );
     41 * // returns ~0.617
     42 *
     43 * @example
     44 * var y = cdf( 21.0, 20.0, 0.5 );
     45 * // returns ~0.622
     46 *
     47 * @example
     48 * var y = cdf( 5.0, 10.0, 0.4 );
     49 * // returns ~0.034
     50 *
     51 * @example
     52 * var y = cdf( 0.0, 10.0, 0.9 );
     53 * // returns ~0.349
     54 *
     55 * @example
     56 * var y = cdf( 21.0, 15.5, 0.5 );
     57 * // returns ~0.859
     58 *
     59 * @example
     60 * var y = cdf( 5.0, 7.4, 0.4 );
     61 * // returns ~0.131
     62 *
     63 * @example
     64 * var y = cdf( 2.0, 0.0, 0.5 );
     65 * // returns NaN
     66 *
     67 * @example
     68 * var y = cdf( 2.0, -2.0, 0.5 );
     69 * // returns NaN
     70 *
     71 * @example
     72 * var y = cdf( NaN, 20.0, 0.5 );
     73 * // returns NaN
     74 *
     75 * @example
     76 * var y = cdf( 0.0, NaN, 0.5 );
     77 * // returns NaN
     78 *
     79 * @example
     80 * var y = cdf( 0.0, 20.0, NaN );
     81 * // returns NaN
     82 *
     83 * @example
     84 * var y = cdf( 2.0, 20, -1.0 );
     85 * // returns NaN
     86 *
     87 * @example
     88 * var y = cdf( 2.0, 20, 1.5 );
     89 * // returns NaN
     90 */
     91 function cdf( x, r, p ) {
     92 	var xint;
     93 	if (
     94 		isnan( x ) ||
     95 		isnan( r ) ||
     96 		isnan( p ) ||
     97 		r <= 0.0 ||
     98 		p < 0.0 ||
     99 		p > 1.0
    100 	) {
    101 		return NaN;
    102 	}
    103 	if ( x < 0.0 ) {
    104 		return 0.0;
    105 	}
    106 	if ( x === PINF ) {
    107 		return 1.0;
    108 	}
    109 	// Ensure left-continuity:
    110 	xint = floor( x + 1e-7 );
    111 	return betainc( p, r, xint + 1.0 );
    112 }
    113 
    114 
    115 // EXPORTS //
    116 
    117 module.exports = cdf;