@stdlib/stats-base-dists-normal-entropy/lib/main.js

Normal distribution differential entropy.

/**
* @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 ln = require( '@stdlib/math-base-special-ln' );
var TWO_PI = require( '@stdlib/constants-float64-two-pi' );
var E = require( '@stdlib/constants-float64-e' );


// MAIN //

/**
* Returns the differential entropy for a normal distribution with mean `mu` and standard deviation `sigma`.
*
* @param {number} mu - mean
* @param {PositiveNumber} sigma - standard deviation
* @returns {number} entropy
*
* @example
* var y = entropy( 0.0, 1.0 );
* // returns ~1.419
*
* @example
* var y = entropy( 5.0, 3.0 );
* // returns ~2.518
*
* @example
* var y = entropy( NaN, 1.0 );
* // returns NaN
*
* @example
* var y = entropy( 0.0, NaN );
* // returns NaN
*
* @example
* var y = entropy( 0.0, 0.0 );
* // returns NaN
*/
function entropy( mu, sigma ) {
	if (
		isnan( mu ) ||
		isnan( sigma ) ||
		sigma <= 0.0
	) {
		return NaN;
	}
	return 0.5 * ln( TWO_PI * E * sigma*sigma );
}


// EXPORTS //

module.exports = entropy;