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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 isNonNegativeInteger = require( '@stdlib/math/base/assert/is-nonnegative-integer' );
var ibetaDerivative = require( './ibeta_derivative.js' );
// MAIN //
/**
* Evaluates the probability mass function (PMF) for a negative binomial distribution with number of successes until experiment is stopped `r` and success probability `p`.
*
* @param {number} x - input value
* @param {PositiveNumber} r - number of successes until experiment is stopped
* @param {Probability} p - success probability
* @returns {Probability} evaluated PMF
*
* @example
* var y = pmf( 5.0, 20.0, 0.8 );
* // returns ~0.157
*
* @example
* var y = pmf( 21.0, 20.0, 0.5 );
* // returns ~0.06
*
* @example
* var y = pmf( 5.0, 10.0, 0.4 );
* // returns ~0.016
*
* @example
* var y = pmf( 0.0, 10.0, 0.9 );
* // returns ~0.349
*
* @example
* var y = pmf( 21.0, 15.5, 0.5 );
* // returns ~0.037
*
* @example
* var y = pmf( 5.0, 7.4, 0.4 );
* // returns ~0.051
*
* @example
* var y = pmf( 2.0, 0.0, 0.5 );
* // returns NaN
*
* @example
* var y = pmf( 2.0, -2.0, 0.5 );
* // returns NaN
*
* @example
* var y = pmf( 2.0, 20, -1.0 );
* // returns NaN
*
* @example
* var y = pmf( 2.0, 20, 1.5 );
* // returns NaN
*
* @example
* var y = pmf( NaN, 20.0, 0.5 );
* // returns NaN
*
* @example
* var y = pmf( 0.0, NaN, 0.5 );
* // returns NaN
*
* @example
* var y = pmf( 0.0, 20.0, NaN );
* // returns NaN
*/
function pmf( x, r, p ) {
if (
isnan( x ) ||
isnan( r ) ||
isnan( p ) ||
r <= 0.0 ||
p <= 0.0 ||
p > 1.0
) {
return NaN;
}
if ( !isNonNegativeInteger( x ) || p === 0.0 ) {
return 0.0;
}
return ( p / ( r + x ) ) * ibetaDerivative( p, r, x + 1.0 );
}
// EXPORTS //
module.exports = pmf;
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