factory.js (1922B)
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 constantFunction = require( '@stdlib/utils/constant-function' ); 24 var isnan = require( '@stdlib/math/base/assert/is-nan' ); 25 var beta = require( '@stdlib/math/base/special/beta' ); 26 var sqrt = require( '@stdlib/math/base/special/sqrt' ); 27 var pow = require( '@stdlib/math/base/special/pow' ); 28 29 30 // MAIN // 31 32 /** 33 * Returns a function for evaluating the probability density function (PDF) for a Student's t distribution with `v` degrees of freedom. 34 * 35 * @param {PositiveNumber} v - degrees of freedom 36 * @returns {Function} PDF 37 * 38 * @example 39 * var pdf = factory( 1.0 ); 40 * var y = pdf( 3.0 ); 41 * // returns ~0.032 42 * 43 * y = pdf( 1.0 ); 44 * // returns ~0.159 45 */ 46 function factory( v ) { 47 var exponent; 48 var betaTerm; 49 50 if ( isnan( v ) || v <= 0 ) { 51 return constantFunction( NaN ); 52 } 53 betaTerm = sqrt( v ) * beta( v/2.0, 0.5 ); 54 exponent = ( 1.0 + v ) / 2.0; 55 return pdf; 56 57 /** 58 * Evaluates the probability density function (PDF) for a Student's t distribution. 59 * 60 * @private 61 * @param {number} x - input value 62 * @returns {number} evaluated PDF 63 * 64 * @example 65 * var y = pdf( 2.3 ); 66 * // returns <number> 67 */ 68 function pdf( x ) { 69 if ( isnan( x ) ) { 70 return NaN; 71 } 72 return pow( v / ( v + pow( x, 2.0 ) ), exponent ) / betaTerm; 73 } 74 } 75 76 77 // EXPORTS // 78 79 module.exports = factory;