The Negative Hypergeometric Distribution: Discussion on Theoretical Results and Applications

2021 ◽  
pp. 117-125
Author(s):  
W. H. Moolman
Keyword(s):  
Hypergeometric Distribution ◽  
Negative Hypergeometric Distribution ◽  
Theoretical Results

Battleship and the negative hypergeometric distribution

2018 ◽  
Vol 41 (1) ◽  
pp. 3-7 ◽  
Author(s):  
Melanie A. Autin ◽  
Natasha E. Gerstenschlager
Keyword(s):  
Hypergeometric Distribution ◽  
Negative Hypergeometric Distribution

scholarly journals Refining One Theorem For The Romanovsky Distribution

2021 ◽  
Vol 03 (06) ◽  
pp. 103-108
Author(s):  
Yusupova A.K. ◽  
◽  
Gafforov R.A. ◽  
Keyword(s):  
Asymptotic Method ◽  
Hypergeometric Distribution ◽  
Negative Hypergeometric Distribution ◽  
Erlang Distributions

The paper considered a refinement of the theorem for a negative-hypergeometric distribution( the Romanovsky distribution), i.e., convergence over variation of the Romanovsky distribution by Erlang distributions. The theorem is proved by the direct asymptotic method.

An Improved Negative Binomial Approximation for Negative Hypergeometric Distribution

2013 ◽  
Vol 427-429 ◽  
pp. 2549-2553 ◽  
Author(s):  
Dong Ping Hu ◽  
Yong Quan Cui ◽  
Ai Hua Yin
Keyword(s):  
Negative Binomial ◽  
Hypergeometric Distribution ◽  
Numerical Examples ◽  
Negative Hypergeometric Distribution ◽  
Binomial Approximation ◽  
Negative Binomial Approximation ◽  
Better Than

This paper gives an improved negative binomial approximation for negative hypergeometric probability. Some numerical examples are presented to illustrate that in most practical cases the effect of our approximation is almost uniformly better than the negative binomial approximation.

scholarly journals Expectation Identity of the Hypergeometric Distribution and Its Application in the Calculations of High-Order Origin Moments

2021 ◽  
Author(s):  
Yuan-Quan Wang ◽  
Ying-Ying Zhang ◽  
Jia-Lei Liu
Keyword(s):  
Stirling Numbers ◽  
High Order ◽  
Hypergeometric Distribution ◽  
Novel Method ◽  
Theoretical Results

Abstract We provide a novel method to analytically calculate the high-order origin moments of a hypergeometric distribution, that is, the expectation identity method. First, the expectation identity of the hypergeometric distribution is discovered and summarized in a theorem. After that, we analytically calculate the first four origin moments of the hypergeometric distribution by using the expectation identity. Furthermore, we analytically calculate the general kth (k=1,2,…) origin moment of the hypergeometric distribution by using the expectation identity, and the results are summarized in a theorem. Moreover, we use the general kth origin moment to validate the first four origin moments of the hypergeometric distribution. Next, the coefficients of the first ten origin moments of the hypergeometric distribution are summarized in a table containing Stirling numbers of the second kind. Moreover, the general kth origin moment of the hypergeometric distribution by using the expectation identity is restated by another theorem involving Stirling numbers of the second kind. Finally, we provide some numerical and theoretical results.

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