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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 betaCDF = require( '@stdlib/stats/base/dists/beta/cdf' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var PINF = require( '@stdlib/constants/float64/pinf' );
// MAIN //
/**
* Evaluates the cumulative distribution function (CDF) for a beta prime distribution with first shape parameter `alpha` and second shape parameter `beta` at a value `x`.
*
* @param {number} x - input value
* @param {PositiveNumber} alpha - first shape parameter
* @param {PositiveNumber} beta - second shape parameter
* @returns {Probability} evaluated CDF
*
* @example
* var y = cdf( 0.5, 1.0, 1.0 );
* // returns ~0.333
*
* @example
* var y = cdf( 0.5, 2.0, 4.0 );
* // returns ~0.539
*
* @example
* var y = cdf( 0.2, 2.0, 2.0 );
* // returns ~0.074
*
* @example
* var y = cdf( 0.8, 4.0, 4.0 );
* // returns ~0.38
*
* @example
* var y = cdf( -0.5, 4.0, 2.0 );
* // returns 0.0
*
* @example
* var y = cdf( 2.0, -1.0, 0.5 );
* // returns NaN
*
* @example
* var y = cdf( 2.0, 0.5, -1.0 );
* // returns NaN
*
* @example
* var y = cdf( NaN, 1.0, 1.0 );
* // returns NaN
*
* @example
* var y = cdf( 0.0, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = cdf( 0.0, 1.0, NaN );
* // returns NaN
*/
function cdf( x, alpha, beta ) {
if (
isnan( x ) ||
isnan( alpha ) ||
isnan( beta ) ||
alpha <= 0.0 ||
beta <= 0.0
) {
return NaN;
}
if ( x <= 0.0 ) {
return 0.0;
}
if ( x === PINF ) {
return 1.0;
}
return betaCDF( x / ( 1.0 + x ), alpha, beta );
}
// EXPORTS //
module.exports = cdf;
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