@stdlib/stats/base/dists/discrete-uniform/mgf/lib/factory.js

Standard library statistical functions.

/**
* @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 constantFunction = require( '@stdlib/utils/constant-function' );
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 //

/**
* Returns a function for evaluating the moment-generating function (MGF) of a discrete uniform distribution with minimum support `a` and maximum support `b`.
*
* @param {integer} a - minimum support
* @param {integer} b - maximum support
* @returns {Function} MGF
*
* @example
* var mgf = factory( 6, 7 );
* var y = mgf( 0.1 );
* // returns ~1.918
*
* y = mgf( 1.1 );
* // returns ~1471.722
*/
function factory( a, b ) {
	var n;
	if (
		isnan( a ) ||
		isnan( b ) ||
		!isInteger( a ) ||
		!isInteger( b ) ||
		a > b
	) {
		return constantFunction( NaN );
	}
	n = b - a + 1;
	return mgf;

	/**
	* Evaluates the moment-generating function (MGF) of a discrete uniform distribution.
	*
	* @private
	* @param {number} t - input value
	* @returns {number} evaluated MGF
	*
	* @example
	* var y = mgf( 0.5 );
	* // returns <number>
	*/
	function mgf( t ) {
		var ret;
		if ( isnan( t ) ) {
			return NaN;
		}
		if ( t === 0.0 ) {
			return 1.0;
		}
		// Case: t not equal to zero
		ret = exp( t*a ) * expm1( t*n );
		ret /= n * expm1( t );
		return ret;
	}
}


// EXPORTS //

module.exports = factory;