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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 constantFunction = require( '@stdlib/utils/constant-function' );
var degenerate = require( '@stdlib/stats/base/dists/degenerate/logcdf' ).factory;
var normalLogcdf = require( '@stdlib/stats/base/dists/normal/logcdf' );
var log1pexp = require( '@stdlib/math/base/special/log1pexp' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var NINF = require( '@stdlib/constants/float64/ninf' );
// MAIN //
/**
* Returns a function for evaluating the natural logarithm of the cumulative distribution function (CDF) for a Wald distribution.
*
* @param {PositiveNumber} mu - mean
* @param {NonNegativeNumber} lambda - shape parameter
* @returns {Function} function to evaluate the natural logarithm of the cumulative distribution function
*
* @example
* var logcdf = factory( 1.0, 1.0 );
* var y = logcdf( 2.0 );
* // returns ~-0.122
*
* y = logcdf( 0.5 );
* // returns ~-1.008
*/
function factory( mu, lambda ) {
var c;
if (
isnan( mu ) ||
isnan( lambda ) ||
mu <= 0.0 ||
lambda < 0.0
) {
return constantFunction( NaN );
}
if ( lambda === 0.0 ) {
return degenerate( mu );
}
c = ( 2.0 * lambda ) / mu;
return logcdf;
/**
* Evaluates the natural logarithm of the cumulative distribution function (CDF) of a Wald distribution.
*
* @private
* @param {number} x - input value
* @returns {number} evaluated logCDF
*
* @example
* var y = logcdf( 2.0 );
* // returns <number>
*/
function logcdf( x ) {
var a;
var b;
var v;
var z;
if ( isnan( x ) ) {
return NaN;
}
if ( x <= 0.0 ) {
return NINF;
}
if ( x === PINF ) {
return 0.0;
}
z = sqrt( lambda / x );
v = x / mu;
// First term: ln( Φ( √(λ/x)·(x/μ-1) ) ):
a = normalLogcdf( z * ( v - 1.0 ), 0.0, 1.0 );
// Second term, in log-space to avoid overflow of exp( 2λ/μ ):
b = c + normalLogcdf( -z * ( v + 1.0 ), 0.0, 1.0 );
// Sum the terms in log-space: ln( e^a + e^b ) = a + ln( 1 + e^(b-a) ):
return a + log1pexp( b - a );
}
}
// EXPORTS //
module.exports = factory;
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