cdf.js (1800B)
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 isnan = require( '@stdlib/math/base/assert/is-nan' ); 24 var exp = require( '@stdlib/math/base/special/exp' ); 25 var pow = require( '@stdlib/math/base/special/pow' ); 26 27 28 // MAIN // 29 30 /** 31 * Evaluates the cumulative distribution function (CDF) for a Rayleigh distribution with scale parameter `sigma` at a value `x`. 32 * 33 * @param {number} x - input value 34 * @param {NonNegativeNumber} sigma - scale parameter 35 * @returns {Probability} evaluated CDF 36 * 37 * @example 38 * var y = cdf( 2.0, 3.0 ); 39 * // returns ~0.199 40 * 41 * @example 42 * var y = cdf( 1.0, 2.0 ); 43 * // returns ~0.118 44 * 45 * @example 46 * var y = cdf( -1.0, 4.0 ); 47 * // returns 0.0 48 * 49 * @example 50 * var y = cdf( NaN, 1.0 ); 51 * // returns NaN 52 * 53 * @example 54 * var y = cdf( 0.0, NaN ); 55 * // returns NaN 56 * 57 * @example 58 * // Negative scale parameter: 59 * var y = cdf( 2.0, -1.0 ); 60 * // returns NaN 61 */ 62 function cdf( x, sigma ) { 63 var s2; 64 if ( 65 isnan( x ) || 66 isnan( sigma ) || 67 sigma < 0.0 68 ) { 69 return NaN; 70 } 71 if ( sigma === 0.0 ) { 72 return ( x < 0.0 ) ? 0.0 : 1.0; 73 } 74 if ( x < 0.0 ) { 75 return 0.0; 76 } 77 s2 = pow( sigma, 2.0 ); 78 return 1.0 - exp( -pow( x, 2.0 ) / ( 2.0 * s2 ) ); 79 } 80 81 82 // EXPORTS // 83 84 module.exports = cdf;