cdf.js (1767B)
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 exp = require( '@stdlib/math/base/special/exp' ); 25 26 27 // MAIN // 28 29 /** 30 * Evaluates the cumulative distribution function (CDF) for a Laplace distribution with location parameter `mu` and scale parameter `b` at value `x`. 31 * 32 * @param {number} x - input value 33 * @param {number} mu - location parameter 34 * @param {PositiveNumber} b - scale parameter 35 * @returns {Probability} evaluated CDF 36 * 37 * @example 38 * var y = cdf( 2.0, 0.0, 1.0 ); 39 * // returns ~0.932 40 * 41 * @example 42 * var y = cdf( 5.0, 10.0, 3.0 ); 43 * // returns ~0.094 44 * 45 * @example 46 * var y = cdf( NaN, 0.0, 1.0 ); 47 * // returns NaN 48 * 49 * @example 50 * var y = cdf( 2, NaN, 1.0 ); 51 * // returns NaN 52 * 53 * @example 54 * var y = cdf( 2.0, 0.0, NaN ); 55 * // returns NaN 56 * 57 * @example 58 * // Negative scale parameter: 59 * var y = cdf( 2.0, 0.0, -1.0 ); 60 * // returns NaN 61 */ 62 function cdf( x, mu, b ) { 63 var z; 64 if ( 65 isnan( x ) || 66 isnan( mu ) || 67 isnan( b ) || 68 b <= 0.0 69 ) { 70 return NaN; 71 } 72 z = ( x - mu ) / b; 73 if ( x < mu ) { 74 return 0.5 * exp( z ); 75 } 76 return 1.0 - ( 0.5 * exp( -z ) ); 77 } 78 79 80 // EXPORTS // 81 82 module.exports = cdf;