logpdf.js (1951B)
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 ln = require( '@stdlib/math/base/special/ln' ); 25 var LN_TWO_PI = require( '@stdlib/constants/float64/ln-two-pi' ); 26 var NINF = require( '@stdlib/constants/float64/ninf' ); 27 28 29 // MAIN // 30 31 /** 32 * Evaluates the natural logarithm of the probability density function (PDF) for a Lévy distribution with location parameter `mu` and scale parameter `c` at a value `x`. 33 * 34 * @param {number} x - input value 35 * @param {number} mu - location parameter 36 * @param {PositiveNumber} c - scale parameter 37 * @returns {number} evaluated logPDF 38 * 39 * @example 40 * var y = logpdf( 2.0, 0.0, 1.0 ); 41 * // returns ~-2.209 42 * 43 * @example 44 * var y = logpdf( -1.0, 4.0, 2.0 ); 45 * // returns -Infinity 46 * 47 * @example 48 * var y = logpdf( NaN, 0.0, 1.0 ); 49 * // returns NaN 50 * 51 * @example 52 * var y = logpdf( 0.0, NaN, 1.0 ); 53 * // returns NaN 54 * 55 * @example 56 * var y = logpdf( 0.0, 0.0, NaN ); 57 * // returns NaN 58 * 59 * @example 60 * // Negative scale parameter: 61 * var y = logpdf( 2.0, 0.0, -1.0 ); 62 * // returns NaN 63 */ 64 function logpdf( x, mu, c ) { 65 var z; 66 if ( 67 isnan( x ) || 68 isnan( mu ) || 69 isnan( c ) || 70 c <= 0.0 71 ) { 72 return NaN; 73 } 74 if ( x <= mu ) { 75 return NINF; 76 } 77 z = x - mu; 78 return 0.5 * ( ln( c ) - LN_TWO_PI - ( c/z ) - ( 3.0*ln( z ) ) ); 79 } 80 81 82 // EXPORTS // 83 84 module.exports = logpdf;