factory.js (1876B)
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 constantFunction = require( '@stdlib/utils/constant-function' ); 24 var isnan = require( '@stdlib/math/base/assert/is-nan' ); 25 var atan2 = require( '@stdlib/math/base/special/atan2' ); 26 27 28 // VARIABLES // 29 30 var ONE_OVER_PI = 0.3183098861837907; 31 32 33 // MAIN // 34 35 /** 36 * Returns a function for evaluating the cumulative distribution function (CDF) for a Cauchy distribution with location parameter `x0` and scale parameter `gamma`. 37 * 38 * @param {number} x0 - location parameter 39 * @param {PositiveNumber} gamma - scale parameter 40 * @returns {Function} CDF 41 * 42 * @example 43 * var cdf = factory( 10.0, 2.0 ); 44 * 45 * var y = cdf( 10.0 ); 46 * // returns 0.5 47 * 48 * y = cdf( 12.0 ); 49 * // returns 0.75 50 */ 51 function factory( x0, gamma ) { 52 if ( 53 isnan( gamma ) || 54 isnan( x0 ) || 55 gamma <= 0.0 56 ) { 57 return constantFunction( NaN ); 58 } 59 return cdf; 60 61 /** 62 * Evaluates the cumulative distribution function (CDF) for a Cauchy distribution. 63 * 64 * @private 65 * @param {number} x - input value 66 * @returns {Probability} evaluated CDF 67 * 68 * @example 69 * var y = cdf( 2.0 ); 70 * // returns <number> 71 */ 72 function cdf( x ) { 73 if ( isnan( x ) ) { 74 return NaN; 75 } 76 return ( ONE_OVER_PI * atan2( x-x0, gamma ) ) + 0.5; 77 } 78 } 79 80 81 // EXPORTS // 82 83 module.exports = factory;