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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.
*
*
* ## Notice
*
* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_62_0/boost/math/special_functions/detail/t_distribution_inv.hpp}. The implementation has been modified for JavaScript.
*
* ```text
* Copyright John Maddock 2006.
* Copyright Paul A. Bristow 2007.
*
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt)
* ```
*/
'use strict';
// MODULES //
var inverseStudentsT = require( './inverse_students_t.js' );
// MAIN //
/**
* Returns the inverse of the incomplete beta function via the Student t distribution.
*
* @private
* @param {PositiveNumber} a - function parameter
* @param {Probability} p - probability value
* @param {Object} py - placeholder object holding one minus the returned value
* @returns {number} function value
*/
function findIBetaInvFromTDist( a, p, py ) {
var df;
var u;
var v;
var t;
u = p / 2.0;
v = 1.0 - u;
df = a * 2.0;
t = inverseStudentsT( df, u, v );
if ( py ) {
py.value = t * t / ( df + ( t*t ) );
}
return df / ( df + ( t*t ) );
}
// EXPORTS //
module.exports = findIBetaInvFromTDist;
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