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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 kernelBetaincinv = require( '@stdlib/math/base/special/kernel-betaincinv' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var sign = require( '@stdlib/math/base/special/signum' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
// MAIN //
/**
* Evaluates the quantile function for a Student's t distribution with degrees of freedom `v` at a probability `p`.
*
* @param {Probability} p - input value
* @param {PositiveNumber} v - degrees of freedom
* @returns {number} evaluated quantile function
*
* @example
* var y = quantile( 0.8, 1.0 );
* // returns ~1.376
*
* @example
* var y = quantile( 0.1, 1.0 );
* // returns ~-3.078
*
* @example
* var y = quantile( 0.5, 0.1 );
* // returns 0.0
*
* @example
* var y = quantile( -0.2, 0.1 );
* // returns NaN
*
* @example
* var y = quantile( NaN, 1.0 );
* // returns NaN
*
* @example
* var y = quantile( 0.0, NaN );
* // returns NaN
*
* @example
* var y = quantile( 0.5, -1.0 );
* // returns NaN
*/
function quantile( p, v ) {
var prob;
var xs;
if (
isnan( v ) ||
isnan( p ) ||
v <= 0.0 ||
p < 0.0 ||
p > 1.0
) {
return NaN;
}
prob = ( p > 0.5 ) ? 1.0 - p : p;
xs = kernelBetaincinv( v / 2.0, 0.5, 2.0 * prob, 1.0 - (2.0 * prob) );
return sign( p - 0.5 ) * sqrt( v * xs[ 1 ] / xs[ 0 ] );
}
// EXPORTS //
module.exports = quantile;
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