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.

scholarly journals Distribution of the combinatorial multisets component vectors

2012 ◽  
Vol 53 ◽  
Author(s):  
Eugenijus Manstavičius ◽  
Robertas Petuchovas
Keyword(s):  
Total Variation ◽  
Negative Binomial ◽  
Random Variables ◽  
Total Variation Distance ◽  
Equal Probability ◽  
Combinatorial Structures ◽  
Variation Distance ◽  
Dependent Coordinates ◽  
Binomial Random Variables

We explore a class of random combinatorial structures called weighted multisets. Their components are taken from an initial set satisfying general boundedness conditions posed on the number of elements with a given weight. The component vector of a multiset of weight n taken with equal probability has dependent coordinates, nevertheless, up to r = o(n) of them as n→∞, we approximate by an appropriate vector comprised from independent negative binomial random variables. The main result is an estimate of the total variation distance.

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