@stdlib/stats-base-dists-f-variance/lib/main.js

F distribution variance.

/**
* @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 pow = require( '@stdlib/math-base-special-pow' );


// MAIN //

/**
* Returns the variance of an F distribution.
*
* @param {PositiveNumber} d1 - numerator degrees of freedom
* @param {PositiveNumber} d2 - denominator degrees of freedom
* @returns {PositiveNumber} variance
*
* @example
* var v = variance( 3.0, 5.0 );
* // returns ~11.111
*
* @example
* var v = variance( 4.0, 12.0 );
* // returns ~1.26
*
* @example
* var v = variance( 8.0, 5.0 );
* // returns ~7.639
*
* @example
* var v = variance( 1.0, 4.0 );
* // returns NaN
*
* @example
* var v = variance( 1.0, -0.1 );
* // returns NaN
*
* @example
* var v = variance( -0.1, 1.0 );
* // returns NaN
*
* @example
* var v = variance( 2.0, NaN );
* // returns NaN
*
* @example
* var v = variance( NaN, 2.0 );
* // returns NaN
*/
function variance( d1, d2 ) {
	var out;
	if ( d1 <= 0.0 || d2 <= 4.0 ) {
		return NaN;
	}
	out = 2.0 * d2 * d2 * ( d1 + d2 - 2.0 );
	out /= d1 * pow( d2 - 2.0, 2.0 ) * ( d2 - 4.0 );
	return out;
}


// EXPORTS //

module.exports = variance;