Press n or j to go to the next uncovered block, b, p or k for the previous block.
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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 PINF = require( '@stdlib/constants/float64/pinf' );
var ibetaDerivative = require( './ibeta_derivative.js' );
// MAIN //
/**
* Evaluates the probability density function (PDF) for an F distribution with numerator degrees of freedom `d1` and denominator degrees of freedom `d2` at a value `x`.
*
* @param {number} x - input value
* @param {PositiveNumber} d1 - numerator degrees of freedom
* @param {PositiveNumber} d2 - denominator degrees of freedom
* @returns {number} evaluated PDF
*
* @example
* var y = pdf( 2.0, 0.5, 1.0 );
* // returns ~0.057
*
* @example
* var y = pdf( 0.1, 1.0, 1.0 );
* // returns ~0.915
*
* @example
* var y = pdf( -1.0, 4.0, 2.0 );
* // returns 0.0
*
* @example
* var y = pdf( NaN, 1.0, 1.0 );
* // returns NaN
*
* @example
* var y = pdf( 0.0, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = pdf( 0.0, 1.0, NaN );
* // returns NaN
*
* @example
* var y = pdf( 2.0, 1.0, -1.0 );
* // returns NaN
*
* @example
* var y = pdf( 2.0, -1.0, 1.0 );
* // returns NaN
*/
function pdf( x, d1, d2 ) {
var v1x;
var y;
var z;
if (
isnan( x ) ||
isnan( d1 ) ||
isnan( d2 ) ||
d1 <= 0.0 ||
d2 <= 0.0
) {
return NaN;
}
if ( x < 0.0 || x === PINF ) {
return 0.0;
}
if ( x === 0.0 ) {
if ( d1 < 2.0 ) {
return PINF;
}
if ( d1 === 2.0 ) {
return 1.0;
}
return 0.0;
}
v1x = d1 * x;
if ( v1x > d2 ) {
y = ( d2 * d1 ) / ( ( d2 + v1x ) * ( d2 + v1x ) );
return y * ibetaDerivative( d2 / ( d2+v1x ), d2/2.0, d1/2.0 );
}
z = d2 + v1x;
y = ((z * d1) - (x * d1 * d1)) / ( z * z );
return y * ibetaDerivative( v1x / ( d2+v1x ), d1/2.0, d2/2.0 );
}
// EXPORTS //
module.exports = pdf;
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