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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 trunc = require( '@stdlib/math/base/special/trunc' );
var max = require( '@stdlib/math/base/special/max' );
var min = require( '@stdlib/math/base/special/min' );
var pmf = require( '@stdlib/stats/base/dists/hypergeometric/pmf' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var Float64Array = require( '@stdlib/array/float64' );
var sum = require( './sum.js' );
// MAIN //
/**
* Evaluates the cumulative distribution function (CDF) for a hypergeometric distribution with population size `N`, subpopulation size `K`, and number of draws `n` at a value `x`.
*
* @param {number} x - input value
* @param {NonNegativeInteger} N - population size
* @param {NonNegativeInteger} K - subpopulation size
* @param {NonNegativeInteger} n - number of draws
* @returns {Probability} evaluated CDF
*
* @example
* var y = cdf( 1.0, 8, 4, 2 );
* // returns ~0.786
*
* @example
* var y = cdf( 1.5, 8, 4, 2 );
* // returns ~0.786
*
* @example
* var y = cdf( 2.0, 8, 4, 2 );
* // returns 1.0
*
* @example
* var y = cdf( 0, 8, 4, 2 );
* // returns ~0.214
*
* @example
* var y = cdf( NaN, 10, 5, 2 );
* // returns NaN
*
* @example
* var y = cdf( 0.0, NaN, 5, 2 );
* // returns NaN
*
* @example
* var y = cdf( 0.0, 10, NaN, 2 );
* // returns NaN
*
* @example
* var y = cdf( 0.0, 10, 5, NaN );
* // returns NaN
*
* @example
* var y = cdf( 2.0, 10.5, 5, 2 );
* // returns NaN
*
* @example
* var y = cdf( 2.0, 10, 1.5, 2 );
* // returns NaN
*
* @example
* var y = cdf( 2.0, 10, 5, -2.0 );
* // returns NaN
*
* @example
* var y = cdf( 2.0, 10, 5, 12 );
* // returns NaN
*
* @example
* var y = cdf( 2.0, 8, 3, 9 );
* // returns NaN
*/
function cdf( x, N, K, n ) {
var denom;
var probs;
var num;
var ret;
var i;
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;
}
x = trunc( x );
if ( x < max( 0, n+K-N ) ) {
return 0.0;
}
if ( x >= min( n, K ) ) {
return 1.0;
}
probs = new Float64Array( x+1 );
probs[ x ] = pmf( x, N, K, n );
/*
* Use recurrence relation:
*
* (x+1)( N - K - (n-x-1))P(X=x+1)=(K-x)(n-x)P(X=x)
*/
for ( i = x-1; i >= 0; i-- ) {
num = ( i+1 ) * ( N-K-(n-i-1) );
denom = ( K-i ) * ( n-i );
probs[ i ] = ( num/denom ) * probs[ i+1 ];
}
ret = sum( probs );
return min( ret, 1.0 );
}
// EXPORTS //
module.exports = cdf;
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