Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 | 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 1017x 1017x 1017x 1017x 1017x 1017x 1017x 1017x 1017x 1002x 1017x 17x 17x 1000x 1000x 1000x 1017x 2x 2x 2x 2x 2x | /**
* @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 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 //
/**
* Evaluates the moment-generating function (MGF) for a Wald distribution with mean `mu` and shape parameter `lambda` at a value `t`.
*
* @param {number} t - input value
* @param {PositiveNumber} mu - mean
* @param {PositiveNumber} lambda - shape parameter
* @returns {number} evaluated MGF
*
* @example
* var y = mgf( 0.1, 2.0, 3.0 );
* // returns ~1.2405
*
* @example
* var y = mgf( -1.0, 0.5, 2.0);
* //returns ~0.6237
*
* @example
* var y = mgf ( NaN, 0.5, 2.0);
* // returns NaN
*
* @example
* var y = mgf ( 0.1, NaN, 2.0);
* // returns NaN
*
* @example
* var y = mgf ( 0.1, 0.5, NaN);
* // returns NaN
*
* @example
* var y = mgf ( 0.1, -1.0, 2.0);
* // returns NaN
*
* @example
* var y = mgf ( 0.1, 0.5, -2.0);
* // returns NaN
*
* @example
* var y = mgf ( 1.0, 2.0, 3.0);
* // returns NaN
*/
function mgf( t, mu, lambda ) {
var mu2Lambda;
var lambdaMu;
if (
isnan( t ) ||
isnan( mu ) ||
isnan( lambda ) ||
mu <= 0.0 ||
lambda <= 0.0 ||
t > lambda / ( 2.0 * pow( mu, 2.0 ) )
) {
return NaN;
}
lambdaMu = lambda / mu;
mu2Lambda = 2.0 * pow( mu, 2.0 ) / lambda;
return exp( lambdaMu * ( 1.0 - sqrt( 1.0 - ( mu2Lambda * t ) ) ) );
}
// EXPORTS //
module.exports = mgf;
|