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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 exp = require( '@stdlib/math/base/special/exp' );
var pow = require( '@stdlib/math/base/special/pow' );
// MAIN //
/**
* Evaluates the moment-generating function (MGF) for a triangular distribution with lower limit `a`, upper limit `b`, and mode `c` at a value `t`.
*
* @param {number} t - input value
* @param {number} a - lower limit
* @param {number} b - upper limit
* @param {number} c - mode
* @returns {number} evaluated MGF
*
* @example
* var y = mgf( 0.5, -1.0, 1.0, 0.0 );
* // returns ~1.021
*
* @example
* var y = mgf( 0.5, -1.0, 1.0, 0.5 );
* // returns ~1.111
*
* @example
* var y = mgf( -0.3, -20.0, 0.0, -2.0 );
* // returns ~24.334
*
* @example
* var y = mgf( -2.0, -1.0, 1.0, 0.0 );
* // returns ~1.381
*
* @example
* var y = mgf( NaN, 0.0, 1.0, 0.5 );
* // returns NaN
*
* @example
* var y = mgf( 0.0, NaN, 1.0, 0.5 );
* // returns NaN
*
* @example
* var y = mgf( 0.0, 0.0, NaN, 0.5 );
* // returns NaN
*
* @example
* var y = mgf( 0.5, 1.0, 0.0, NaN );
* // returns NaN
*
* @example
* var y = mgf( 0.5, 1.0, 0.0, 1.5 );
* // returns NaN
*/
function mgf( t, a, b, c ) {
var bmc;
var bma;
var cma;
var ret;
if (
isnan( t ) ||
isnan( a ) ||
isnan( b ) ||
isnan( c ) ||
a > c ||
c > b
) {
return NaN;
}
if ( t === 0.0 ) {
return 1.0;
}
bmc = b - c;
bma = b - a;
cma = c - a;
ret = ( bmc * exp( a*t ) ) - ( bma * exp( c*t ) );
ret += cma * exp( b*t );
ret *= 2.0;
ret /= bma * cma * bmc * pow( t, 2.0 );
return ret;
}
// EXPORTS //
module.exports = mgf;
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