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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 constantFunction = require( '@stdlib/utils/constant-function' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var ln = require( '@stdlib/math/base/special/ln' );
// MAIN //
/**
* Returns a function for evaluating the quantile function for a Laplace distribution with location parameter `mu` and scale parameter `b`.
*
* @param {number} mu - location parameter
* @param {PositiveNumber} b - scale parameter
* @returns {Function} quantile function
*
* @example
* var quantile = factory( 10.0, 2.0 );
* var y = quantile( 0.5 );
* // returns 10.0
*
* y = quantile( 0.8 );
* // returns ~11.833
*/
function factory( mu, b ) {
if (
isnan( mu ) ||
isnan( b ) ||
b <= 0.0
) {
return constantFunction( NaN );
}
return quantile;
/**
* Evaluates the quantile function for a Laplace distribution.
*
* @private
* @param {Probability} p - input value
* @returns {number} evaluated quantile function
*
* @example
* var y = quantile( 0.3 );
* // returns <number>
*/
function quantile( p ) {
if ( isnan( p ) || p < 0.0 || p > 1.0 ) {
return NaN;
}
// Work with the tail probability (`p` or `1-p`, which is exact for `p >= 0.5`) rather than `1 - 2|p-0.5|`, which rounds away the low-order bits of a small `p`:
if ( p < 0.5 ) {
return mu + ( b * ln( 2.0*p ) );
}
return mu - ( b * ln( 2.0*(1.0-p) ) );
}
}
// EXPORTS //
module.exports = factory;
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