logcdf.js (2040B)
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 erfc = require( '@stdlib/math/base/special/erfc' ); 25 var sqrt = require( '@stdlib/math/base/special/sqrt' ); 26 var NINF = require( '@stdlib/constants/float64/ninf' ); 27 var ln = require( '@stdlib/math/base/special/ln' ); 28 29 30 // MAIN // 31 32 /** 33 * Evaluates the logarithm of the cumulative distribution function (CDF) for a Lévy distribution with location parameter `mu` and scale parameter `c` at value `x`. 34 * 35 * @param {number} x - input value 36 * @param {number} mu - location parameter 37 * @param {PositiveNumber} c - scale parameter 38 * @returns {number} evaluated logCDF 39 * 40 * @example 41 * var y = logcdf( 2.0, 0.0, 1.0 ); 42 * // returns ~-0.735 43 * 44 * @example 45 * var y = logcdf( 12.0, 10.0, 3.0 ); 46 * // returns ~-1.51 47 * 48 * @example 49 * var y = logcdf( 9.0, 10.0, 3.0 ); 50 * // returns -Infinity 51 * 52 * @example 53 * var y = logcdf( NaN, 0.0, 1.0 ); 54 * // returns NaN 55 * 56 * @example 57 * var y = logcdf( 2, NaN, 1.0 ); 58 * // returns NaN 59 * 60 * @example 61 * var y = logcdf( 2.0, 0.0, NaN ); 62 * // returns NaN 63 * 64 * @example 65 * // Negative scale parameter: 66 * var y = logcdf( 2.0, 0.0, -1.0 ); 67 * // returns NaN 68 */ 69 function logcdf( x, mu, c ) { 70 var z; 71 if ( 72 isnan( x ) || 73 isnan( mu ) || 74 isnan( c ) || 75 c <= 0.0 76 ) { 77 return NaN; 78 } 79 if ( x < mu ) { 80 return NINF; 81 } 82 z = sqrt( c / ( 2.0 * ( x-mu ) ) ); 83 return ln( erfc( z ) ); 84 } 85 86 87 // EXPORTS // 88 89 module.exports = logcdf;