Limit distributions for the maxima of discrete random variables under monotone normalization

2021 ◽  
Author(s):  
Kosto V. Mitov ◽  
Saralees Nadarajah
Keyword(s):  
Random Variables ◽  
Limit Distributions ◽  
Discrete Random Variables

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

scholarly journals The number of failed components in a coherent working system when the lifetimes are discretely distributed

Metrika ◽  
2021 ◽  
Author(s):  
Krzysztof Jasiński
Keyword(s):  
Random Variables ◽  
Continuous Case ◽  
Coherent System ◽  
Coherent Systems ◽  
Discrete Random Variables ◽  
Independent And Identically Distributed

AbstractIn this paper, we study the number of failed components of a coherent system. We consider the case when the component lifetimes are discrete random variables that may be dependent and non-identically distributed. Firstly, we compute the probability that there are exactly i, $$i=0,\ldots ,n-k,$$ i = 0 , … , n - k , failures in a k-out-of-n system under the condition that it is operating at time t. Next, we extend this result to other coherent systems. In addition, we show that, in the most popular model of independent and identically distributed component lifetimes, the obtained probability corresponds to the respective one derived in the continuous case and existing in the literature.

Two-stage stochastic programming problems involving interval discrete random variables

OPSEARCH ◽  
2012 ◽  
Vol 49 (3) ◽  
pp. 280-298 ◽  
Author(s):  
Suresh Kumar Barik ◽  
Mahendra Prasad Biswal ◽  
Debashish Chakravarty
Keyword(s):  
Stochastic Programming ◽  
Random Variables ◽  
Two Stage ◽  
Discrete Random Variables

Discrete Random Variables

2016 ◽  
pp. 133-185
Author(s):  
William M. Mendenhall ◽  
Terry L. Sincich
Keyword(s):  
Random Variables ◽  
Discrete Random Variables
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