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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 isnan = require( '@stdlib/math/base/assert/is-nan' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var exp = require( '@stdlib/math/base/special/exp' );
var pow = require( '@stdlib/math/base/special/pow' );
// MAIN //
/**
* Returns a function for evaluating the moment-generating function (MGF) of a Wald distribution with mean `mu` and shape parameter `lambda`.
*
* @param {PositiveNumber} mu - mean
* @param {PositiveNumber} lambda - shape parameter
* @returns {Function} MGF
*
* @example
* var mgf = factory( 2.0, 3.0 );
*
* var y = mgf( 0.1 );
* // returns ~1.2405
*
* y = mgf( 0.2 );
* // returns ~1.6085
*/
function factory( mu, lambda ) {
var mu2Lambda;
var lambdaMu;
if (
isnan( mu ) ||
isnan( lambda ) ||
mu <= 0.0 ||
lambda <= 0.0
) {
return constantFunction( NaN );
}
lambdaMu = lambda / mu;
mu2Lambda = 2.0 * pow( mu, 2.0 ) / lambda;
return mgf;
/**
* Evaluates the moment-generating function (MGF) for a Wald distribution.
*
* @private
* @param {number} t - input value
* @returns {number} evaluated MGF
*
* @example
* var y = mgf( 0.1 );
* // returns <number>
*/
function mgf( t ) {
if (
isnan( t ) ||
t > lambda / ( 2.0 * pow( mu, 2.0 ) )
) {
return NaN;
}
return exp( lambdaMu * ( 1.0 - sqrt( 1.0 - ( mu2Lambda * t ) ) ) );
}
}
// EXPORTS //
module.exports = factory;
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