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@stdlib/stats

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Standard library statistical functions.

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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 gamma = require( '@stdlib/math/base/special/gamma' ); var pow = require( '@stdlib/math/base/special/pow' ); var PINF = require( '@stdlib/constants/float64/pinf' ); // MAIN // /** * Returns the skewness for a Fréchet distribution with shape `alpha`, scale `s`, and location `m`. * * @param {PositiveNumber} alpha - shape parameter * @param {PositiveNumber} s - scale parameter * @param {number} m - location parameter * @returns {PositiveNumber} skewness * * @example * var y = skewness( 5.0, 2.0, 0.0 ); * // returns ~3.535 * * @example * var y = skewness( 5.0, 2.0, -5.0 ); * // returns ~3.535 * * @example * var y = skewness( 1.0, 1.0, 0.0 ); * // returns Infinity * * @example * var y = skewness( NaN, 1.0, 0.0 ); * // returns NaN * * @example * var y = skewness( 1.0, NaN, 0.0 ); * // returns NaN * * @example * var y = skewness( 1.0, 1.0, NaN ); * // returns NaN */ function skewness( alpha, s, m ) { var g1s; var g1; var g2; var g3; if ( isnan( alpha ) || isnan( s ) || isnan( m ) || alpha <= 0.0 || s <= 0.0 ) { return NaN; } if ( alpha <= 3.0 ) { // Case: 0 < alpha <= 3 return PINF; } g1 = gamma( 1.0 - ( 1.0/alpha ) ); g1s = g1*g1; g2 = gamma( 1.0 - ( 2.0/alpha ) ); g3 = gamma( 1.0 - ( 3.0/alpha ) ); return ( g3 - ( 3.0*g2*g1 ) + ( 2.0*g1s*g1 ) ) / pow( g2 - g1s, 1.5 ); } // EXPORTS // module.exports = skewness;