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* @license Apache-2.0
*
* Copyright (c) 2022 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/assert/is-positive-integer' ).isPrimitive;
var prange = require( '@stdlib/stats/base/dists/studentized-range/cdf' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var abs = require( '@stdlib/math/base/special/abs' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var qtrngo = require( './qtrngo.js' );
// VARIABLES //
var PCUT = 1e-8;
var JMAX = 28;
// MAIN //
/**
* Evaluates the quantile function for a studentized range distribution at probability `p` with `r` samples and `v` degrees of freedom.
*
* ## References
*
* - Ferreira, D. F., Demetrico, C. G. B., Manly, B. F. J., and Machado, A. de A. 2007. "Quantis da distribuição do máximo da amplitude estudentizada." _Rev. Mat. Est._, São Paulo, 25 (1): 117-135. <http://jaguar.fcav.unesp.br/RME/fasciculos/v25/v25_n1/A8_Daniel.pdf>.
*
* @param {Probability} p - input probability
* @param {PositiveNumber} r - sample size for range (same for each group; must be greater than or equal to `2`)
* @param {PositiveNumber} v - degrees of freedom (must be greater than or equal to `2`)
* @param {PositiveInteger} [nranges=1] - number of groups whose maximum range is considered
* @returns {number} evaluated quantile function
*
* @example
* var y = qrange( 0.5, 3.0, 2.0 );
* // returns ~1.908
*
* @example
* var y = qrange( 0.9, 17.0, 2.0 );
* // returns ~11.237
*
* @example
* var y = qrange( 0.5, 3.0, 2.0, 2 );
* // returns ~2.549
*/
function qrange( p, r, v, nranges ) {
var aux;
var e1;
var e2;
var q1;
var q2;
var p1;
var p2;
var j;
if (
isnan( r ) ||
isnan( v ) ||
r < 2.0 ||
v < 2.0
) {
return NaN;
}
if ( isnan( p ) || p < 0.0 || p > 1.0 ) {
return NaN;
}
if ( p === 0.0 ) {
return 0.0;
}
if ( p === 1.0 ) {
return PINF;
}
if ( nranges === void 0 ) {
nranges = 1;
}
else if ( !isPositiveInteger( nranges ) ) {
return NaN;
}
q1 = qtrngo( p, v, r );
while ( true ) {
p1 = prange( q1, r, v, nranges );
if ( p1 > p ) {
q1 -= 0.4;
}
if ( q1 < 0.0 ) {
q1 = 0.1;
}
if ( p1 < p ) {
break;
}
}
aux = q1;
if ( abs( p1 - p ) < PCUT ) {
return NaN;
}
q2 = q1 + 0.5;
while ( true ) {
p2 = prange( q2, r, v, nranges );
if ( p2 < p ) {
q2 += 0.4;
}
if ( q2 < 0.0 ) {
q2 = 1.0;
}
if ( p2 > p ) {
break;
}
}
if ( q2 < q1 ) {
q2 = q1 + 0.01;
}
j = 2;
while ( j <= JMAX ) {
p2 = prange( q2, r, v, nranges );
e1 = p1 - p;
e2 = p2 - p;
if ( e2 - e1 !== 0 ) {
aux = ( ( e2 * q1 ) - ( e1 * q2 ) ) / ( e2 - e1 );
}
if ( abs( e1 ) < abs( e2 ) ) {
if ( abs( p1 - p ) < PCUT * 5.0 ) {
j = JMAX + 2;
}
q1 = aux;
p1 = prange( q1, r, v, nranges );
} else {
q1 = q2;
p1 = p2;
q2 = aux;
}
j += 1;
}
return aux;
}
// EXPORTS //
module.exports = qrange;
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