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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 constantFunction = require( '@stdlib/utils/constant-function' );
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 //
/**
* Returns a function for evaluating the probability mass function (PMF) for a hypergeometric distribution with population size `N`, subpopulation size `K`, and number of draws `n`.
*
* @param {NonNegativeInteger} N - population size
* @param {NonNegativeInteger} K - subpopulation size
* @param {NonNegativeInteger} n - number of draws
* @returns {Function} PMF
*
* @example
* var mypmf = factory( 30, 20, 5 );
* var y = mypmf( 4.0 );
* // returns ~0.34
*
* y = mypmf( 1.0 );
* // returns ~0.029
*/
function factory( N, K, n ) {
var maxs;
var mins;
if (
isnan( N ) ||
isnan( K ) ||
isnan( n ) ||
!isNonNegativeInteger( N ) ||
!isNonNegativeInteger( K ) ||
!isNonNegativeInteger( n ) ||
N === PINF ||
K === PINF ||
K > N ||
n > N
) {
return constantFunction( NaN );
}
mins = max( 0, n + K - N );
maxs = min( K, n );
return pmf;
/**
* Evaluates the probability mass function (PMF) for a hypergeometric distribution.
*
* @private
* @param {number} x - input value
* @returns {Probability} evaluated PMF
*/
function pmf( x ) {
var ldenom;
var lnum;
var lpmf;
if ( isnan( x ) ) {
return NaN;
}
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 = factory;
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