A range reduction method for generating discrete random variables

Efraim Shmerling

doi:10.1016/j.spl.2013.01.002

A range reduction method for generating discrete random variables

Statistics & Probability Letters ◽

10.1016/j.spl.2013.01.002 ◽

2013 ◽

Vol 83 (4) ◽

pp. 1094-1099 ◽

Cited By ~ 2

Author(s):

Efraim Shmerling

Keyword(s):

Reduction Method ◽

Random Variables ◽

Range Reduction ◽

Discrete Random Variables

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Normal approximations to discrete unimodal distributions

Journal of Applied Probability ◽

10.1017/s0021900200115931 ◽

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.

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

Metrika ◽

10.1007/s00184-021-00817-2 ◽

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.

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