A Non-uniform Bound on Negative Binomial Approximation via Stein’s Method and z-functions

2018 ◽  
Vol 43 (1) ◽  
pp. 519-536
Author(s):  
K. Jaioun ◽  
W. Panichkitkosolkul ◽  
K. Teerapabolarn
Keyword(s):  
Negative Binomial ◽  
Stein’S Method ◽  
Uniform Bound ◽  
Stein's Method ◽  
Binomial Approximation ◽  
Negative Binomial Approximation

scholarly journals Power Laws in Preferential Attachment Graphs and Stein's Method for the Negative Binomial Distribution

2013 ◽  
Vol 45 (03) ◽  
pp. 876-893 ◽  
Author(s):  
Nathan Ross
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Preferential Attachment ◽  
Power Laws ◽  
Rates Of Convergence ◽  
Stein’S Method ◽  
Stein's Method ◽  
Power Law Distribution ◽  
New Formulation

For a family of linear preferential attachment graphs, we provide rates of convergence for the total variation distance between the degree of a randomly chosen vertex and an appropriate power law distribution as the number of vertices tends to ∞. Our proof uses a new formulation of Stein's method for the negative binomial distribution, which stems from a distributional transformation that has the negative binomial distributions as the only fixed points.

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.

Sign in / Sign up

Export Citation Format

Share Document