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* @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 exp = require( '@stdlib/math/base/special/exp' );
// MAIN //
/**
* Returns the excess kurtosis for a lognormal distribution with location `mu` and scale `sigma`.
*
* @param {number} mu - location parameter
* @param {PositiveNumber} sigma - scale parameter
* @returns {number} excess kurtosis
*
* @example
* var y = kurtosis( 0.0, 1.0 );
* // returns ~110.936
*
* @example
* var y = kurtosis( 5.0, 2.0 );
* // returns ~9220556.977
*
* @example
* var y = kurtosis( NaN, 1.0 );
* // returns NaN
*
* @example
* var y = kurtosis( 0.0, NaN );
* // returns NaN
*
* @example
* var y = kurtosis( 0.0, 0.0 );
* // returns NaN
*/
function kurtosis( mu, sigma ) {
var out;
var s2;
if (
isnan( mu ) ||
isnan( sigma ) ||
sigma <= 0.0
) {
return NaN;
}
s2 = sigma * sigma;
out = exp( 4.0*s2 );
out += 2.0 * exp( 3.0*s2 );
out += 3.0 * exp( 2.0*s2 );
out -= 6.0;
return out;
}
// EXPORTS //
module.exports = kurtosis;
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