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* @license Apache-2.0
*
* Copyright (c) 2020 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 isPositiveInteger = require( '@stdlib/math/base/assert/is-positive-integer' );
var isfinite = require( '@stdlib/math/base/assert/is-finite' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var exp = require( '@stdlib/math/base/special/exp' );
var LN2 = require( '@stdlib/constants/float64/ln-two' );
var weights = require( './weights.js' );
// MAIN //
/**
* Evaluates the quantile function of the Wilcoxon signed rank test statistic with `n` observations.
*
* @param {Probability} p - input value
* @param {PositiveInteger} n - number of observations
* @returns {NonNegativeInteger} evaluated quantile function
*
* @example
* var y = quantile( 0.8, 5 );
* // returns 11
*
* @example
* var y = quantile( 0.5, 4 );
* // returns 5
*
* @example
* var y = quantile( 1.1, 5 );
* // returns NaN
*
* @example
* var y = quantile( -0.2, 5 );
* // returns NaN
*
* @example
* var y = quantile( NaN, 5 );
* // returns NaN
*
* @example
* var y = quantile( 0.0, NaN );
* // returns NaN
*/
function quantile( p, n ) {
var pui;
var q;
var r;
if ( isnan( n ) || !isPositiveInteger( n ) || !isfinite( n ) ) {
return NaN;
}
if ( isnan( p ) || p < 0.0 || p > 1.0 ) {
return NaN;
}
if ( p === 0.0 ) {
return 0;
}
if ( p === 1.0 ) {
return ( n * ( n + 1 ) ) / 2;
}
pui = exp( -n * LN2 );
r = 0;
q = -1;
while ( r < p ) {
q += 1;
r += pui * weights( q, n );
}
return q;
}
// EXPORTS //
module.exports = quantile;
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