logpdf.js (2105B)
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 gammaln = require( '@stdlib/math/base/special/gammaln' ); 25 var ln = require( '@stdlib/math/base/special/ln' ); 26 var NINF = require( '@stdlib/constants/float64/ninf' ); 27 var PINF = require( '@stdlib/constants/float64/pinf' ); 28 var LN2 = require( '@stdlib/constants/float64/ln-two' ); 29 30 31 // MAIN // 32 33 /** 34 * Evaluates the natural logarithm of the probability density function (PDF) for a chi distribution with degrees of freedom `k` at a value `x`. 35 * 36 * @param {number} x - input value 37 * @param {NonNegativeNumber} k - degrees of freedom 38 * @returns {number} evaluated logPDF 39 * 40 * @example 41 * var y = logpdf( 0.3, 4.0 ); 42 * // returns ~-4.35 43 * 44 * @example 45 * var y = logpdf( 0.7, 0.7 ); 46 * // returns ~-0.622 47 * 48 * @example 49 * var y = logpdf( -1.0, 0.5 ); 50 * // returns -Infinity 51 * 52 * @example 53 * var y = logpdf( 0.0, NaN ); 54 * // returns NaN 55 * 56 * @example 57 * var y = logpdf( NaN, 2.0 ); 58 * // returns NaN 59 * 60 * @example 61 * // Negative degrees of freedom: 62 * var y = logpdf( 2.0, -1.0 ); 63 * // returns NaN 64 */ 65 function logpdf( x, k ) { 66 var out; 67 var kh; 68 if ( 69 isnan( x ) || 70 isnan( k ) || 71 k < 0.0 72 ) { 73 return NaN; 74 } 75 if ( k === 0.0 ) { 76 // Point mass at 0... 77 return ( x === 0.0 ) ? PINF : NINF; 78 } 79 if ( x < 0.0 || x === PINF ) { 80 return NINF; 81 } 82 kh = k / 2.0; 83 out = ( ( 1.0-kh ) * LN2 ) + ( ( k-1.0 ) * ln( x ) ) - ( (x*x) / 2.0 ); 84 out -= gammaln( kh ); 85 return out; 86 } 87 88 89 // EXPORTS // 90 91 module.exports = logpdf;