pdf.js (1753B)
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 beta = require( '@stdlib/math/base/special/beta' ); 25 var sqrt = require( '@stdlib/math/base/special/sqrt' ); 26 var pow = require( '@stdlib/math/base/special/pow' ); 27 28 29 // MAIN // 30 31 /** 32 * Evaluates the probability density function (PDF) for a Student's t distribution with degrees of freedom `v` at a value `x`. 33 * 34 * @param {number} x - input value 35 * @param {PositiveNumber} v - degrees of freedom 36 * @returns {number} evaluated PDF 37 * 38 * @example 39 * var y = pdf( 0.3, 4.0 ); 40 * // returns ~0.355 41 * 42 * @example 43 * var y = pdf( 2.0, 0.7 ); 44 * // returns ~0.058 45 * 46 * @example 47 * var y = pdf( -1.0, 0.5 ); 48 * // returns ~0.118 49 * 50 * @example 51 * var y = pdf( 0.0, NaN ); 52 * // returns NaN 53 * 54 * @example 55 * var y = pdf( NaN, 2.0 ); 56 * // returns NaN 57 * 58 * @example 59 * var y = pdf( 2.0, -1.0 ); 60 * // returns NaN 61 */ 62 function pdf( x, v ) { 63 var betaTerm; 64 if ( 65 isnan( x ) || 66 isnan( v ) || 67 v <= 0.0 68 ) { 69 return NaN; 70 } 71 betaTerm = sqrt( v ) * beta( v/2.0, 0.5 ); 72 return pow( v / ( v + pow( x, 2.0 ) ), (1.0+v) / 2.0 ) / betaTerm; 73 } 74 75 76 // EXPORTS // 77 78 module.exports = pdf;