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* @license Apache-2.0
*
* Copyright (c) 2018 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 isInteger = require( '@stdlib/math/base/assert/is-integer' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var expm1 = require( '@stdlib/math/base/special/expm1' );
var exp = require( '@stdlib/math/base/special/exp' );
// MAIN //
/**
* Evaluates the moment-generating function (MGF) of a discrete uniform distribution with minimum support `a` and maximum support `b` at a value `t`.
*
* @param {number} t - input value
* @param {integer} a - minimum support
* @param {integer} b - maximum support
* @returns {number} evaluated MGF
*
* @example
* var y = mgf( 2.0, 0, 4 );
* // returns ~689.475
*
* @example
* var y = mgf( -0.2, 0, 4 );
* // returns ~0.697
*
* @example
* var y = mgf( 2.0, 0, 1 );
* // returns ~4.195
*
* @example
* var y = mgf( 0.5, 3, 3 );
* // returns ~4.482
*
* @example
* var y = mgf( 0.5, 3, 2 );
* // returns NaN
*
* @example
* var y = mgf( NaN, 0, 1 );
* // returns NaN
*
* @example
* var y = mgf( 0.0, NaN, 1 );
* // returns NaN
*
* @example
* var y = mgf( 0.0, 0, NaN );
* // returns NaN
*/
function mgf( t, a, b ) {
var ret;
var n;
if (
isnan( t ) ||
isnan( a ) ||
isnan( b ) ||
!isInteger( a ) ||
!isInteger( b ) ||
a > b
) {
return NaN;
}
if ( t === 0.0 ) {
return 1.0;
}
// Case: t not equal to zero
n = b - a + 1;
ret = exp( t*a ) * expm1( t*n );
ret /= n * expm1( t );
return ret;
}
// EXPORTS //
module.exports = mgf;
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