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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 isnan = require( '@stdlib/math/base/assert/is-nan' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
// MAIN //
/**
* Evaluates the quantile function for a triangular distribution with lower limit `a` and upper limit `b` and mode `c` at a probability `p`.
*
* @param {Probability} p - input value
* @param {number} a - lower limit
* @param {number} b - upper limit
* @param {number} c - mode
* @returns {number} evaluated quantile function
*
* @example
* var y = quantile( 0.9, -1.0, 1.0, 0.0 );
* // returns ~0.553
*
* @example
* var y = quantile( 0.1, -1.0, 1.0, 0.5 );
* // returns ~-0.452
*
* @example
* var y = quantile( 0.1, -20.0, 0.0, -2.0 );
* // returns -14.0
*
* @example
* var y = quantile( 0.8, 0.0, 20.0, 0.0 );
* // returns ~11.056
*
* @example
* var y = quantile( 1.1, -1.0, 1.0, 0.0 );
* // returns NaN
*
* @example
* var y = quantile( -0.1, -1.0, 1.0, 0.0 );
* // returns NaN
*
* @example
* var y = quantile( NaN, 0.0, 1.0, 0.5 );
* // returns NaN
*
* @example
* var y = quantile( 0.3, NaN, 1.0, 0.5 );
* // returns NaN
*
* @example
* var y = quantile( 0.3, 0.0, NaN, 0.5 );
* // returns NaN
*
* @example
* var y = quantile( 0.3, 1.0, 0.0, NaN );
* // returns NaN
*
* @example
* var y = quantile( 0.3, 1.0, 0.0, 1.5 );
* // returns NaN
*/
function quantile( p, a, b, c ) {
var pInflection;
var fact1;
var fact2;
if (
isnan( p ) ||
isnan( a ) ||
isnan( b ) ||
isnan( c ) ||
a > c ||
c > b ||
p < 0.0 ||
p > 1.0
) {
return NaN;
}
pInflection = ( c - a ) / ( b - a );
fact1 = ( b - a ) * ( c - a);
fact2 = ( b - a ) * ( b - c );
if ( p < pInflection ) {
return a + sqrt( fact1 * p );
}
if ( p > pInflection ) {
return b - sqrt( fact2 * ( 1.0 - p ) );
}
// Case: p = pInflection
return c;
}
// EXPORTS //
module.exports = quantile;
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