logcdf.js (2209B)
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 ln = require( '@stdlib/math/base/special/ln' ); 27 var LN_PI = require( '@stdlib/constants/float64/ln-pi' ); 28 var NINF = require( '@stdlib/constants/float64/ninf' ); 29 var LN2 = require( '@stdlib/constants/float64/ln-two' ); 30 31 32 // MAIN // 33 34 /** 35 * Evaluates the logarithm of the cumulative distribution function (CDF) for an arcsine distribution with minimum support `a` and maximum support `b` at a value `x`. 36 * 37 * @param {number} x - input value 38 * @param {number} a - minimum support 39 * @param {number} b - maximum support 40 * @returns {number} evaluated logCDF 41 * 42 * @example 43 * var y = logcdf( 9.0, 0.0, 10.0 ); 44 * // returns ~-0.23 45 * 46 * @example 47 * var y = logcdf( 0.5, 0.0, 2.0 ); 48 * // returns ~-1.1 49 * 50 * @example 51 * var y = logcdf( +Infinity, 2.0, 4.0 ); 52 * // returns 0.0 53 * 54 * @example 55 * var y = logcdf( -Infinity, 2.0, 4.0 ); 56 * // returns -Infinity 57 * 58 * @example 59 * var y = logcdf( NaN, 0.0, 1.0 ); 60 * // returns NaN 61 * 62 * @example 63 * var y = logcdf( 0.0, NaN, 1.0 ); 64 * // returns NaN 65 * 66 * @example 67 * var y = logcdf( 0.0, 0.0, NaN ); 68 * // returns NaN 69 * 70 * @example 71 * var y = logcdf( 2.0, 1.0, 0.0 ); 72 * // returns NaN 73 */ 74 function logcdf( x, a, b ) { 75 if ( 76 isnan( x ) || 77 isnan( a ) || 78 isnan( b ) || 79 a >= b 80 ) { 81 return NaN; 82 } 83 if ( x < a ) { 84 return NINF; 85 } 86 if ( x >= b ) { 87 return 0.0; 88 } 89 return LN2 - LN_PI + ln( asin( sqrt( ( x-a ) / ( b-a ) ) ) ); 90 } 91 92 93 // EXPORTS // 94 95 module.exports = logcdf;