logpdf.js (1880B)
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 betaln = require( '@stdlib/math/base/special/betaln' ); 25 var sqrt = require( '@stdlib/math/base/special/sqrt' ); 26 var pow = require( '@stdlib/math/base/special/pow' ); 27 var ln = require( '@stdlib/math/base/special/ln' ); 28 29 30 // MAIN // 31 32 /** 33 * Evaluates the natural logarithm of the probability density function (PDF) for a Student's t distribution with degrees of freedom `v` at a value `x`. 34 * 35 * @param {number} x - input value 36 * @param {PositiveNumber} v - degrees of freedom 37 * @returns {number} evaluated logPDF 38 * 39 * @example 40 * var y = logpdf( 0.3, 4.0 ); 41 * // returns ~-1.036 42 * 43 * @example 44 * var y = logpdf( 2.0, 0.7 ); 45 * // returns ~-2.841 46 * 47 * @example 48 * var y = logpdf( -1.0, 0.5 ); 49 * // returns ~-2.134 50 * 51 * @example 52 * var y = logpdf( 0.0, NaN ); 53 * // returns NaN 54 * 55 * @example 56 * var y = logpdf( NaN, 2.0 ); 57 * // returns NaN 58 * 59 * @example 60 * var y = logpdf( 2.0, -1.0 ); 61 * // returns NaN 62 */ 63 function logpdf( x, v ) { 64 var betaTerm; 65 if ( 66 isnan( x ) || 67 isnan( v ) || 68 v <= 0.0 69 ) { 70 return NaN; 71 } 72 betaTerm = ln( sqrt( v ) ) + betaln( v/2.0, 0.5 ); 73 return ( ( (1.0+v) / 2.0 ) * ln( v / ( v + pow( x, 2.0 ) ) ) ) - betaTerm; 74 } 75 76 77 // EXPORTS // 78 79 module.exports = logpdf;