UNPKG

@stdlib/stats

Version:

Standard library statistical functions.

71 lines (61 loc) 1.61 kB
/** * @license Apache-2.0 * * Copyright (c) 2018 The Stdlib Authors. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ 'use strict'; // MODULES // var isnan = require( '@stdlib/math/base/assert/is-nan' ); var digamma = require( '@stdlib/math/base/special/digamma' ); var sqrt = require( '@stdlib/math/base/special/sqrt' ); var beta = require( '@stdlib/math/base/special/beta' ); var ln = require( '@stdlib/math/base/special/ln' ); // MAIN // /** * Returns the differential entropy of a Student's t distribution. * * @param {PositiveNumber} v - degrees of freedom * @returns {number} entropy * * @example * var v = entropy( 9.0 ); * // returns ~1.533 * * @example * var v = entropy( 2.0 ); * // returns ~1.96 * * @example * var v = entropy( -0.2 ); * // returns NaN * * @example * var v = entropy( NaN ); * // returns NaN */ function entropy( v ) { var out; var vh; if ( isnan( v ) || v <= 0.0 ) { return NaN; } vh = v / 2.0; out = ( v + 1.0 ) / 2.0; out *= digamma( ( 1.0+v ) / 2.0 ) - digamma( vh ); out += ln( sqrt( v ) * beta( vh, 0.5 ) ); return out; } // EXPORTS // module.exports = entropy;