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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 signum = require( '@stdlib/math/base/special/signum' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var abs = require( '@stdlib/math/base/special/abs' );
var ln = require( '@stdlib/math/base/special/ln' );
// MAIN //
/**
* Evaluates the quantile function for a Laplace distribution with location parameter `mu` and scale parameter `b` at a probability `p`.
*
* @param {Probability} p - input value
* @param {number} mu - location parameter
* @param {PositiveNumber} b - scale parameter
* @returns {number} evaluated quantile function
*
* @example
* var y = quantile( 0.8, 0.0, 1.0 );
* // returns ~0.916
*
* @example
* var y = quantile( 0.5, 4.0, 2.0 );
* // returns 4.0
*
* @example
* var y = quantile( 1.1, 0.0, 1.0 );
* // returns NaN
*
* @example
* var y = quantile( -0.2, 0.0, 1.0 );
* // returns NaN
*
* @example
* var y = quantile( NaN, 0.0, 1.0 );
* // returns NaN
*
* @example
* var y = quantile( 0.0, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = quantile( 0.0, 0.0, NaN );
* // returns NaN
*
* @example
* // Negative scale parameter:
* var y = quantile( 0.5, 0.0, -1.0 );
* // returns NaN
*/
function quantile( p, mu, b ) {
if (
isnan( mu ) ||
isnan( b ) ||
isnan( p ) ||
b <= 0.0 ||
p < 0.0 ||
p > 1.0
) {
return NaN;
}
return mu - ( b * signum( p-0.5 ) * ln( 1.0 - ( 2.0 * abs( p-0.5 ) ) ) );
}
// EXPORTS //
module.exports = quantile;
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