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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 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;
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