Press n or j to go to the next uncovered block, b, p or k for the previous block.
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* @license Apache-2.0
*
* Copyright (c) 2026 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 waldCDF = require( '@stdlib/stats/base/dists/wald/cdf' );
var PINF = require( '@stdlib/constants/float64/pinf' );
// VARIABLES //
var MAX_ITERATIONS = 1e4;
// MAIN //
/**
* Bisection method to find the quantile of a Wald distribution with mean `mu` and shape parameter `lambda` at a probability `p`.
*
* @private
* @param {Probability} p - input value
* @param {PositiveNumber} mu - mean
* @param {PositiveNumber} lambda - shape parameter
* @returns {NonNegativeNumber} evaluated quantile function
*/
function bisect( p, mu, lambda ) {
var a;
var b;
var c;
var m;
var n;
if ( p <= 0.0 ) {
return 0.0;
}
if ( p >= 1.0 ) {
return PINF;
}
// Establish an upper bound `b` such that `CDF(b) >= p`, while keeping `a` a lower bound for which `CDF(a) < p`:
a = 0.0;
b = mu;
n = 1;
while ( waldCDF( b, mu, lambda ) < p && n < MAX_ITERATIONS ) {
a = b;
b *= 2.0;
n += 1;
}
// Bisect the interval `[a,b]` until it can no longer be halved in double-precision arithmetic:
n = 1;
m = ( a + b ) / 2.0;
while ( n < MAX_ITERATIONS ) {
m = ( a + b ) / 2.0;
if ( m <= a || m >= b ) {
return m;
}
c = waldCDF( m, mu, lambda );
if ( p > c ) {
a = m;
} else {
b = m;
}
n += 1;
}
return m;
}
// EXPORTS //
module.exports = bisect;
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