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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 degenerate = require( '@stdlib/stats/base/dists/degenerate/cdf' ).factory;
var gammaFactory = require( '@stdlib/stats/base/dists/gamma/cdf' ).factory;
var isnan = require( '@stdlib/math/base/assert/is-nan' );
// MAIN //
/**
* Returns a function for evaluating the cumulative distribution function (CDF) for a chi distribution with degrees of freedom `k`.
*
* @param {NonNegativeNumber} k - degrees of freedom
* @returns {Function} CDF
*
* @example
* var cdf = factory( 3.0 );
*
* var y = cdf( 6.0 );
* // returns ~1.0
*
* y = cdf( 1.5 );
* // returns ~0.478
*/
function factory( k ) {
var gamma;
if ( k === 0.0 ) {
return degenerate( 0.0 );
}
gamma = gammaFactory( k/2.0, 0.5 );
return cdf;
/**
* Evaluates the cumulative distribution function (CDF) for a chi distribution with degrees of freedom `k`.
*
* @private
* @param {number} x - input value
* @returns {Probability} evaluated CDF
*/
function cdf( x ) {
if ( isnan( x ) ) {
return NaN;
}
if ( x < 0.0 ) {
return 0.0;
}
return gamma( x*x );
}
}
// EXPORTS //
module.exports = factory;
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