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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 expm1 = require( '@stdlib/math/base/special/expm1' );
var pow = require( '@stdlib/math/base/special/pow' );
var log1p = require( '@stdlib/math/base/special/log1p' );
// MAIN //
/**
* Evaluates the moment-generating function (MGF) for a negative binomial distribution.
*
* @param {number} t - input value
* @param {PositiveNumber} r - number of successes until experiment is stopped
* @param {Probability} p - success probability
* @returns {number} evaluated MGF
*
* @example
* var y = mgf( 0.05, 20.0, 0.8 );
* // returns ~1.294
*
* @example
* var y = mgf( 0.1, 20.0, 0.9 );
* // returns ~1.265
*
* @example
* var y = mgf( 0.5, 10.0, 0.8 );
* // returns ~5.868
*
* @example
* var y = mgf( 0.1, 0.0, 0.5 );
* // returns NaN
*
* @example
* var y = mgf( 0.1, -2.0, 0.5 );
* // returns NaN
*
* @example
* var y = mgf( NaN, 20.0, 0.5 );
* // returns NaN
*
* @example
* var y = mgf( 0.0, NaN, 0.5 );
* // returns NaN
*
* @example
* var y = mgf( 0.0, 20.0, NaN );
* // returns NaN
*
* @example
* var y = mgf( 0.2, 20, -1.0 );
* // returns NaN
*
* @example
* var y = mgf( 0.2, 20, 1.5 );
* // returns NaN
*/
function mgf( t, r, p ) {
if (
isnan( t ) ||
isnan( r ) ||
isnan( p ) ||
r <= 0.0 ||
p < 0.0 ||
p > 1.0 ||
t >= -log1p( -p )
) {
return NaN;
}
return pow( p / ( p - ((1.0 - p) * expm1( t )) ), r );
}
// EXPORTS //
module.exports = mgf;
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