cdf.js (1764B)
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 atan2 = require( '@stdlib/math/base/special/atan2' ); 25 26 27 // VARIABLES // 28 29 var ONE_OVER_PI = 0.3183098861837907; 30 31 32 // MAIN // 33 34 /** 35 * Evaluates the cumulative distribution function (CDF) for a Cauchy distribution with location parameter `x0` and scale parameter `gamma` at a value `x`. 36 * 37 * @param {number} x - input value 38 * @param {number} x0 - location parameter 39 * @param {PositiveNumber} gamma - scale parameter 40 * @returns {Probability} evaluated CDF 41 * 42 * @example 43 * var y = cdf( 4.0, 0.0, 2.0 ); 44 * // returns ~0.852 45 * 46 * @example 47 * var y = cdf( 1.0, 0.0, 2.0 ); 48 * // returns ~0.648 49 * 50 * @example 51 * var y = cdf( 1.0, 3.0, 2.0 ); 52 * // returns 0.25 53 * 54 * @example 55 * var y = cdf( NaN, 0.0, 2.0 ); 56 * // returns NaN 57 * 58 * @example 59 * var y = cdf( 1.0, 2.0, NaN ); 60 * // returns NaN 61 * 62 * @example 63 * var y = cdf( 1.0, NaN, 3.0 ); 64 * // returns NaN 65 */ 66 function cdf( x, x0, gamma ) { 67 if ( 68 isnan( x ) || 69 isnan( gamma ) || 70 isnan( x0 ) || 71 gamma <= 0.0 72 ) { 73 return NaN; 74 } 75 return ( ONE_OVER_PI * atan2( x-x0, gamma ) ) + 0.5; 76 } 77 78 79 // EXPORTS // 80 81 module.exports = cdf;