time-to-botec

Benchmark sampling in different programming languages
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kurtosis.js (2101B)

      1 /**
      2 * @license Apache-2.0
      3 *
      4 * Copyright (c) 2018 The Stdlib Authors.
      5 *
      6 * Licensed under the Apache License, Version 2.0 (the "License");
      7 * you may not use this file except in compliance with the License.
      8 * You may obtain a copy of the License at
      9 *
     10 *    http://www.apache.org/licenses/LICENSE-2.0
     11 *
     12 * Unless required by applicable law or agreed to in writing, software
     13 * distributed under the License is distributed on an "AS IS" BASIS,
     14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     15 * See the License for the specific language governing permissions and
     16 * limitations under the License.
     17 */
     18 
     19 'use strict';
     20 
     21 // MODULES //
     22 
     23 var isNonNegativeInteger = require( '@stdlib/math/base/assert/is-nonnegative-integer' );
     24 var PINF = require( '@stdlib/constants/float64/pinf' );
     25 
     26 
     27 // MAIN //
     28 
     29 /**
     30 * Returns the excess kurtosis of a hypergeometric distribution.
     31 *
     32 * @param {NonNegativeInteger} N - population size
     33 * @param {NonNegativeInteger} K - subpopulation size
     34 * @param {NonNegativeInteger} n - number of draws
     35 * @returns {number} kurtosis
     36 *
     37 * @example
     38 * var v = kurtosis( 16, 11, 4 );
     39 * // returns ~-0.326
     40 *
     41 * @example
     42 * var v = kurtosis( 4, 2, 2 );
     43 * // returns 0.0
     44 *
     45 * @example
     46 * var v = kurtosis( 10, 5, 12 );
     47 * // returns NaN
     48 *
     49 * @example
     50 * var v = kurtosis( 10.3, 10, 4 );
     51 * // returns NaN
     52 *
     53 * @example
     54 * var v = kurtosis( 10, 5.5, 4 );
     55 * // returns NaN
     56 *
     57 * @example
     58 * var v = kurtosis( 10, 5, 4.5 );
     59 * // returns NaN
     60 *
     61 * @example
     62 * var v = kurtosis( NaN, 10, 4 );
     63 * // returns NaN
     64 *
     65 * @example
     66 * var v = kurtosis( 20, NaN, 4 );
     67 * // returns NaN
     68 *
     69 * @example
     70 * var v = kurtosis( 20, 10, NaN );
     71 * // returns NaN
     72 */
     73 function kurtosis( N, K, n ) {
     74 	var p;
     75 	var q;
     76 	if (
     77 		!isNonNegativeInteger( N ) ||
     78 		!isNonNegativeInteger( K ) ||
     79 		!isNonNegativeInteger( n ) ||
     80 		N === PINF ||
     81 		K === PINF ||
     82 		K > N ||
     83 		n > N
     84 	) {
     85 		return NaN;
     86 	}
     87 	p = ( N-1 ) * ( N*N ) * ( ( N*(N+1) ) - ( 6*K*(N-K) ) - ( 6*n*(N-n) ) );
     88 	p += 6 * n * K * ( N-K ) * ( N-n ) * ( (5*N) - 6 );
     89 	q = n * K * ( N-K ) * ( N-n ) * ( N-2 ) * ( N-3 );
     90 	return p / q;
     91 }
     92 
     93 
     94 // EXPORTS //
     95 
     96 module.exports = kurtosis;