A Non-uniform Bound on Poisson Approximation for Random Sums of Negative Binomial Random Variables

2019 ◽  
Vol 65 (11) ◽  
pp. 99-102
Author(s):  
Kanint Teerapabolarn
Keyword(s):  
Negative Binomial ◽  
Random Variables ◽  
Poisson Approximation ◽  
Uniform Bound ◽  
Random Sums ◽  
Binomial Random Variables

scholarly journals New Bounds on Poisson Approximation for Random Sums of Independent Binomial Random Variables}

2018 ◽  
Vol 7 (4) ◽  
pp. 43
Author(s):  
Giang Truong Le
Keyword(s):  
Random Variables ◽  
Poisson Approximation ◽  
Random Sums ◽  
Binomial Random Variables

In this paper, we use the Stein-Chen method to obtain new bounds on Poisson approximation for random sums of  independent binomial random variables. Some results related to sums of independent binomial distributed random variables are also investigated. The received results in the present study are more general and sharper than some known results.

Ordering comparison of negative binomial random variables with their mixtures

2008 ◽  
Vol 78 (14) ◽  
pp. 2234-2239 ◽  
Author(s):  
Mohammad Hossein Alamatsaz ◽  
Somayyeh Abbasi
Keyword(s):  
Negative Binomial ◽  
Random Variables ◽  
Binomial Random Variables

COMMENTS ON THE SURVEY BY BALAKRISHNAN AND ZHAO

2013 ◽  
Vol 27 (4) ◽  
pp. 445-449 ◽  
Author(s):  
Moshe Shaked
Keyword(s):  
Order Statistics ◽  
Negative Binomial ◽  
Random Variables ◽  
Hazard Rates ◽  
Proportional Hazard ◽  
Stochastic Comparisons ◽  
Exponential Random Variables ◽  
Binomial Random Variables

N. Balakrishnan and Peng Zhao have prepared an outstanding survey of recent results that stochastically compare various order statistics and some ranges based on two collections of independent heterogeneous random variables. Their survey focuses on results for heterogeneous exponential random variables and their extensions to random variables with proportional hazard rates. In addition, some results that stochastically compare order statistics based on heterogeneous gamma, Weibull, geometric, and negative binomial random variables are also given. In particular, the authors of have listed some stochastic comparisons that are based on one heterogeneous collection of random variables, and one homogeneous collection of random variables. Personally, I find these types of comparisons to be quite fascinating. Balakrishnan and Zhao have done a thorough job of listing all the known results of this kind.

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