logcdf.js (2191B)
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 expm1 = require( '@stdlib/math/base/special/expm1' ); 24 var isnan = require( '@stdlib/math/base/assert/is-nan' ); 25 var log1p = require( '@stdlib/math/base/special/log1p' ); 26 var exp = require( '@stdlib/math/base/special/exp' ); 27 var pow = require( '@stdlib/math/base/special/pow' ); 28 var ln = require( '@stdlib/math/base/special/ln' ); 29 var LNHALF = require( '@stdlib/constants/float64/ln-half' ); 30 var NINF = require( '@stdlib/constants/float64/ninf' ); 31 32 33 // MAIN // 34 35 /** 36 * Evaluates the logarithm of the cumulative distribution function (CDF) for a Rayleigh distribution with scale parameter `sigma` at a value `x`. 37 * 38 * @param {number} x - input value 39 * @param {NonNegativeNumber} sigma - scale parameter 40 * @returns {number} evaluated logCDF 41 * 42 * @example 43 * var y = logcdf( 2.0, 3.0 ); 44 * // returns ~-1.613 45 * 46 * @example 47 * var y = logcdf( 1.0, 2.0 ); 48 * // returns ~-2.141 49 * 50 * @example 51 * var y = logcdf( -1.0, 4.0 ); 52 * // returns -Infinity 53 * 54 * @example 55 * var y = logcdf( NaN, 1.0 ); 56 * // returns NaN 57 * 58 * @example 59 * var y = logcdf( 0.0, NaN ); 60 * // returns NaN 61 * 62 * @example 63 * // Negative scale parameter: 64 * var y = logcdf( 2.0, -1.0 ); 65 * // returns NaN 66 */ 67 function logcdf( x, sigma ) { 68 var s2; 69 var p; 70 if ( 71 isnan( x ) || 72 isnan( sigma ) || 73 sigma < 0.0 74 ) { 75 return NaN; 76 } 77 if ( sigma === 0.0 ) { 78 return ( x < 0.0 ) ? NINF : 0.0; 79 } 80 if ( x < 0.0 ) { 81 return NINF; 82 } 83 s2 = pow( sigma, 2.0 ); 84 p = -pow( x, 2.0 ) / ( 2.0 * s2 ); 85 return ( p < LNHALF ) ? log1p( -exp( p ) ) : ln( -expm1( p ) ); 86 } 87 88 89 // EXPORTS // 90 91 module.exports = logcdf;