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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 isNonNegativeInteger = require( '@stdlib/math/base/assert/is-nonnegative-integer' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var exp = require( '@stdlib/math/base/special/exp' );
var fln = require( '@stdlib/math/base/special/factorialln' );
var max = require( '@stdlib/math/base/special/max' );
var min = require( '@stdlib/math/base/special/min' );
var PINF = require( '@stdlib/constants/float64/pinf' );
// MAIN //
/**
* Evaluates the probability mass function (PMF) for a hypergeometric distribution with population size `N`, subpopulation size `K`, and number of draws `n`.
*
* @param {number} x - input value
* @param {NonNegativeInteger} N - population size
* @param {NonNegativeInteger} K - subpopulation size
* @param {NonNegativeInteger} n - number of draws
* @returns {Probability} evaluated PMF
*
* @example
* var y = pmf( 1.0, 8, 4, 2 );
* // returns ~0.571
*
* @example
* var y = pmf( 2.0, 8, 4, 2 );
* // returns ~0.214
*
* @example
* var y = pmf( 0.0, 8, 4, 2 );
* // returns ~0.214
*
* @example
* var y = pmf( 1.5, 8, 4, 2 );
* // returns 0.0
*
* @example
* var y = pmf( NaN, 10, 5, 2 );
* // returns NaN
*
* @example
* var y = pmf( 0.0, NaN, 5, 2 );
* // returns NaN
*
* @example
* var y = pmf( 0.0, 10, NaN, 2 );
* // returns NaN
*
* @example
* var y = pmf( 0.0, 10, 5, NaN );
* // returns NaN
*
* @example
* var y = pmf( 2.0, 10.5, 5, 2 );
* // returns NaN
*
* @example
* var y = pmf( 2.0, 5, 1.5, 2 );
* // returns NaN
*
* @example
* var y = pmf( 2.0, 10, 5, -2.0 );
* // returns NaN
*
* @example
* var y = pmf( 2.0, 10, 5, 12 );
* // returns NaN
*
* @example
* var y = pmf( 2.0, 8, 3, 9 );
* // returns NaN
*/
function pmf( x, N, K, n ) {
var ldenom;
var lnum;
var lpmf;
var maxs;
var mins;
if (
isnan( x ) ||
isnan( N ) ||
isnan( K ) ||
isnan( n ) ||
!isNonNegativeInteger( N ) ||
!isNonNegativeInteger( K ) ||
!isNonNegativeInteger( n ) ||
N === PINF ||
K === PINF ||
K > N ||
n > N
) {
return NaN;
}
mins = max( 0, n + K - N );
maxs = min( K, n );
if (
isNonNegativeInteger( x ) &&
mins <= x &&
x <= maxs
) {
lnum = fln( n ) + fln( K ) + fln( N - n ) + fln( N - K );
ldenom = fln( N ) + fln( x ) + fln( n - x );
ldenom += fln( K - x ) + fln( N - K + x - n );
lpmf = lnum - ldenom;
return exp( lpmf );
}
return 0.0;
}
// EXPORTS //
module.exports = pmf;
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