scholarly journals Stein factors for negative binomial approximation in Wasserstein distance

Bernoulli ◽  
2015 ◽  
Vol 21 (2) ◽  
pp. 1002-1013 ◽  
Author(s):  
A.D. Barbour ◽  
H.L. Gan ◽  
A. Xia
Keyword(s):  
Negative Binomial ◽  
Wasserstein Distance ◽  
Binomial Approximation ◽  
Negative Binomial Approximation

scholarly journals On Negative Binomial Approximation to k-Runs

2008 ◽  
Vol 45 (2) ◽  
pp. 456-471 ◽  
Author(s):  
Xiaoxin Wang ◽  
Aihua Xia
Keyword(s):  
Negative Binomial ◽  
Practical Interest ◽  
Poisson Approximation ◽  
Approximate Model ◽  
Approximation Accuracy ◽  
Compound Poisson Approximation ◽  
Variation Distance ◽  
Binomial Approximation ◽  
Negative Binomial Approximation ◽  
Accuracy Of Approximation

The distributions of the run occurrences for a sequence of independent and identically distributed (i.i.d.) experiments are usually obtained by combinatorial methods (see Balakrishnan and Koutras (2002, Chapter 5)) and the resulting formulae are often very tedious, while the distributions for non i.i.d. experiments are generally intractable. It is therefore of practical interest to find a suitable approximate model with reasonable approximation accuracy. In this paper we demonstrate that the negative binomial distribution is the most suitable approximate model for the number of k-runs: it outperforms the Poisson approximation, the general compound Poisson approximation as observed in Eichelsbacher and Roos (1999), and the translated Poisson approximation in Rollin (2005). In particular, its accuracy of approximation in terms of the total variation distance improves when the number of experiments increases, in the same way as the normal approximation improves in the Berry-Esseen theorem.

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 On Negative Binomial Approximation to k-Runs

2008 ◽  
Vol 45 (02) ◽  
pp. 456-471 ◽  
Author(s):  
Xiaoxin Wang ◽  
Aihua Xia
Keyword(s):  
Negative Binomial ◽  
Practical Interest ◽  
Poisson Approximation ◽  
Approximate Model ◽  
Approximation Accuracy ◽  
Compound Poisson Approximation ◽  
Variation Distance ◽  
Binomial Approximation ◽  
Negative Binomial Approximation ◽  
Accuracy Of Approximation

The distributions of the run occurrences for a sequence of independent and identically distributed (i.i.d.) experiments are usually obtained by combinatorial methods (see Balakrishnan and Koutras (2002, Chapter 5)) and the resulting formulae are often very tedious, while the distributions for non i.i.d. experiments are generally intractable. It is therefore of practical interest to find a suitable approximate model with reasonable approximation accuracy. In this paper we demonstrate that the negative binomial distribution is the most suitable approximate model for the number ofk-runs: it outperforms the Poisson approximation, the general compound Poisson approximation as observed in Eichelsbacher and Roos (1999), and the translated Poisson approximation in Rollin (2005). In particular, its accuracy of approximation in terms of the total variation distance improves when the number of experiments increases, in the same way as the normal approximation improves in the Berry-Esseen theorem.

On Negative Binomial Approximation

2013 ◽  
Vol 57 (1) ◽  
pp. 97-109 ◽  
Author(s):  
P. Vellaisamy ◽  
N. S. Upadhye ◽  
V. Čekanavičius
Keyword(s):  
Negative Binomial ◽  
Binomial Approximation ◽  
Negative Binomial Approximation
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