Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 | 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x | /**
* @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 PINF = require( '@stdlib/constants/float64/pinf' );
// MAIN //
/**
* Returns the excess kurtosis of a hypergeometric distribution.
*
* @param {NonNegativeInteger} N - population size
* @param {NonNegativeInteger} K - subpopulation size
* @param {NonNegativeInteger} n - number of draws
* @returns {number} excess kurtosis
*
* @example
* var v = kurtosis( 16, 11, 4 );
* // returns ~-0.326
*
* @example
* var v = kurtosis( 4, 2, 2 );
* // returns 0.0
*
* @example
* var v = kurtosis( 10, 5, 12 );
* // returns NaN
*
* @example
* var v = kurtosis( 10.3, 10, 4 );
* // returns NaN
*
* @example
* var v = kurtosis( 10, 5.5, 4 );
* // returns NaN
*
* @example
* var v = kurtosis( 10, 5, 4.5 );
* // returns NaN
*
* @example
* var v = kurtosis( NaN, 10, 4 );
* // returns NaN
*
* @example
* var v = kurtosis( 20, NaN, 4 );
* // returns NaN
*
* @example
* var v = kurtosis( 20, 10, NaN );
* // returns NaN
*/
function kurtosis( N, K, n ) {
var p;
var q;
if (
!isNonNegativeInteger( N ) ||
!isNonNegativeInteger( K ) ||
!isNonNegativeInteger( n ) ||
N === PINF ||
K === PINF ||
K > N ||
n > N
) {
return NaN;
}
p = ( N-1 ) * ( N*N ) * ( ( N*(N+1) ) - ( 6*K*(N-K) ) - ( 6*n*(N-n) ) );
p += 6 * n * K * ( N-K ) * ( N-n ) * ( (5*N) - 6 );
q = n * K * ( N-K ) * ( N-n ) * ( N-2 ) * ( N-3 );
return p / q;
}
// EXPORTS //
module.exports = kurtosis;
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