main.js (2060B)
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 asin = require( '@stdlib/math/base/special/asin' ); 25 var sqrt = require( '@stdlib/math/base/special/sqrt' ); 26 var PI = require( '@stdlib/constants/float64/pi' ); 27 28 29 // VARIABLES // 30 31 var TWO_OVER_PI = 2.0 / PI; // TODO: consider moving to pkg 32 33 34 // MAIN // 35 36 /** 37 * Evaluates the cumulative distribution function (CDF) for an arcsine distribution with minimum support `a` and maximum support `b` at a value `x`. 38 * 39 * @param {number} x - input value 40 * @param {number} a - minimum support 41 * @param {number} b - maximum support 42 * @returns {Probability} evaluated CDF 43 * 44 * @example 45 * var y = cdf( 9.0, 0.0, 10.0 ); 46 * // returns ~0.795 47 * 48 * @example 49 * var y = cdf( 0.5, 0.0, 2.0 ); 50 * // returns ~0.333 51 * 52 * @example 53 * var y = cdf( +Infinity, 2.0, 4.0 ); 54 * // returns 1.0 55 * 56 * @example 57 * var y = cdf( -Infinity, 2.0, 4.0 ); 58 * // returns 0.0 59 * 60 * @example 61 * var y = cdf( NaN, 0.0, 1.0 ); 62 * // returns NaN 63 * 64 * @example 65 * var y = cdf( 0.0, NaN, 1.0 ); 66 * // returns NaN 67 * 68 * @example 69 * var y = cdf( 0.0, 0.0, NaN ); 70 * // returns NaN 71 * 72 * @example 73 * var y = cdf( 2.0, 1.0, 0.0 ); 74 * // returns NaN 75 */ 76 function cdf( x, a, b ) { 77 if ( 78 isnan( x ) || 79 isnan( a ) || 80 isnan( b ) || 81 a >= b 82 ) { 83 return NaN; 84 } 85 if ( x < a ) { 86 return 0.0; 87 } 88 if ( x >= b ) { 89 return 1.0; 90 } 91 return TWO_OVER_PI * asin( sqrt( ( x-a ) / ( b-a ) ) ); 92 } 93 94 95 // EXPORTS // 96 97 module.exports = cdf;