@stdlib/stats/base/dists/cosine/mgf/lib/main.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 isnan = require( '@stdlib/math/base/assert/is-nan' );
var sinh = require( '@stdlib/math/base/special/sinh' );
var exp = require( '@stdlib/math/base/special/exp' );
var PI_SQUARED = require( '@stdlib/constants/float64/pi-squared' );


// MAIN //

/**
* Evaluates the moment-generating function (MGF) for a raised cosine distribution with location parameter `mu` and scale parameter `s` at a value `t`.
*
* @param {number} t - input value
* @param {number} mu - location parameter
* @param {PositiveNumber} s - scale parameter
* @returns {number} evaluated MGF
*
* @example
* var y = mgf( 0.5, 0.0, 1.0 );
* // returns ~1.016
*
* @example
* var y = mgf( 1.2, 0.0, 1.0 );
* // returns ~1.098
*
* @example
* var y = mgf( -0.9, 0.0, 3.0 );
* // returns ~1.578
*
* @example
* var y = mgf( 2.0, 0.0, NaN );
* // returns NaN
*
* @example
* var y = mgf( 2.0, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = mgf( NaN, 0.0, 1.0 );
* // returns NaN
*/
function mgf( t, mu, s ) {
	var out;
	var st;
	if (
		isnan( t ) ||
		isnan( mu ) ||
		isnan( s ) ||
		s <= 0.0
	) {
		return NaN;
	}
	st = s * t;
	out = PI_SQUARED * sinh( st );
	out /= st * ( PI_SQUARED + ( st*st ) );
	out *= exp( mu * t );
	return out;
}


// EXPORTS //

module.exports = mgf;