logpdf.js (2033B)
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 log1p = require( '@stdlib/math/base/special/log1p' ); 25 var pow = require( '@stdlib/math/base/special/pow' ); 26 var ln = require( '@stdlib/math/base/special/ln' ); 27 var LNPI = require( '@stdlib/constants/float64/ln-pi' ); 28 29 30 // MAIN // 31 32 /** 33 * Evaluates the natural logarithm of the probability density function (logPDF) for a Cauchy distribution with location parameter `x0` and scale parameter `gamma` at a value `x`. 34 * 35 * @param {number} x - input value 36 * @param {number} x0 - location parameter 37 * @param {PositiveNumber} gamma - scale parameter 38 * @returns {number} evaluated logPDF 39 * 40 * @example 41 * var y = logpdf( 2.0, 1.0, 1.0 ); 42 * // returns ~-1.838 43 * 44 * @example 45 * var y = logpdf( 4.0, 3.0, 0.1 ); 46 * // returns ~-3.457 47 * 48 * @example 49 * var y = logpdf( 4.0, 3.0, 3.0 ); 50 * // returns ~-2.349 51 * 52 * @example 53 * var y = logpdf( NaN, 1.0, 1.0 ); 54 * // returns NaN 55 * 56 * @example 57 * var y = logpdf( 2.0, NaN, 1.0 ); 58 * // returns NaN 59 * 60 * @example 61 * var y = logpdf( 2.0, 1.0, NaN ); 62 * // returns NaN 63 * 64 * @example 65 * // Negative scale parameter: 66 * var y = logpdf( 2.0, 1.0, -2.0 ); 67 * // returns NaN 68 */ 69 function logpdf( x, x0, gamma ) { 70 if ( 71 isnan( x ) || 72 isnan( gamma ) || 73 isnan( x0 ) || 74 gamma <= 0.0 75 ) { 76 return NaN; 77 } 78 return -( LNPI + ln( gamma ) + log1p( pow( (x-x0)/gamma, 2.0 ) ) ); 79 } 80 81 82 // EXPORTS // 83 84 module.exports = logpdf;