Limit laws for kth order statistics from strong-mixing processes

1984 ◽  
Vol 21 (04) ◽  
pp. 720-729 ◽  
Author(s):  
W. Dziubdziela
Keyword(s):  
Weak Convergence ◽  
Order Statistics ◽  
Poisson Distribution ◽  
Sufficient Conditions ◽  
Strong Mixing ◽  
Mixing Processes ◽  
Limit Laws ◽  
Independent Case ◽  
Necessary And Sufficient ◽  
Mixing Sequence

We present necessary and sufficient conditions for the weak convergence of the distributions of the kth order statistics from a strictly stationary strong-mixing sequence of random variables to limit laws which are represented in terms of a compound Poisson distribution. The obtained limit laws form a class larger than that occurring in the independent case.

Limit laws for kth order statistics from strong-mixing processes

1984 ◽  
Vol 21 (4) ◽  
pp. 720-729 ◽  
Author(s):  
W. Dziubdziela
Keyword(s):  
Weak Convergence ◽  
Order Statistics ◽  
Poisson Distribution ◽  
Sufficient Conditions ◽  
Strong Mixing ◽  
Mixing Processes ◽  
Limit Laws ◽  
Independent Case ◽  
Necessary And Sufficient ◽  
Mixing Sequence

We present necessary and sufficient conditions for the weak convergence of the distributions of the kth order statistics from a strictly stationary strong-mixing sequence of random variables to limit laws which are represented in terms of a compound Poisson distribution. The obtained limit laws form a class larger than that occurring in the independent case.

Limit laws for kth order statistics from conditionally mixing arrays of random variables

1986 ◽  
Vol 23 (03) ◽  
pp. 679-687
Author(s):  
W. Dziubdziela
Keyword(s):  
Weak Convergence ◽  
Order Statistics ◽  
Poisson Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Compound Poisson Distribution ◽  
Limit Laws ◽  
Compound Poisson ◽  
Mixed Compound

We present sufficient conditions for the weak convergence of the distributions of thekth order statistics from a conditionally mixing array of random variables to limit laws which are represented in terms of a mixed compound Poisson distribution.

Limit laws for kth order statistics from conditionally mixing arrays of random variables

1986 ◽  
Vol 23 (3) ◽  
pp. 679-687 ◽  
Author(s):  
W. Dziubdziela
Keyword(s):  
Weak Convergence ◽  
Order Statistics ◽  
Poisson Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Compound Poisson Distribution ◽  
Limit Laws ◽  
Compound Poisson ◽  
Mixed Compound

We present sufficient conditions for the weak convergence of the distributions of the kth order statistics from a conditionally mixing array of random variables to limit laws which are represented in terms of a mixed compound Poisson distribution.

Asymptotic behavior of the records of multivariate random sequences in a norm sense

2020 ◽  
Vol 70 (6) ◽  
pp. 1457-1468
Author(s):  
Haroon M. Barakat ◽  
M. H. Harpy
Keyword(s):  
Asymptotic Behavior ◽  
Weak Convergence ◽  
Sufficient Conditions ◽  
Record Values ◽  
Necessary And Sufficient Conditions ◽  
Random Sequences ◽  
Necessary And Sufficient

AbstractIn this paper, we investigate the asymptotic behavior of the multivariate record values by using the Reduced Ordering Principle (R-ordering). Necessary and sufficient conditions for weak convergence of the multivariate record values based on sup-norm are determined. Some illustrative examples are given.

scholarly journals Poisson distribution series on a general class of analytic functions

2020 ◽  
Vol 24 (2) ◽  
pp. 241-251
Author(s):  
Basem A. Frasin
Keyword(s):  
Integral Operator ◽  
Poisson Distribution ◽  
Analytic Functions ◽  
General Class ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Class A ◽  
Poisson Distribution Series ◽  
Necessary And Sufficient

The main object of this paper is to find necessary and sufficient conditions for the Poisson distribution series to be in a general class of analytic functions with negative coefficients. Further, we consider an integral operator related to the Poisson distribution series to be in this class. A number of known or new results are shown to follow upon specializing the parameters involved in our main results.

Order statistics, Poisson processes and repairable systems

1976 ◽  
Vol 13 (03) ◽  
pp. 519-529 ◽  
Author(s):  
Douglas R. Miller
Keyword(s):  
Order Statistics ◽  
Point Processes ◽  
Failure Time ◽  
Sufficient Conditions ◽  
Renewal Processes ◽  
Repairable Systems ◽  
Homogeneous Poisson Process ◽  
Necessary And Sufficient ◽  
Non Homogeneous Poisson Process ◽  
Weibull Process

Necessary and sufficient conditions are presented under which the point processes equivalent to order statistics of n i.i.d. random variables or superpositions of n i.i.d. renewal processes converge to a non-degenerate limiting process as n approaches infinity. The limiting process must be one of three types of non-homogeneous Poisson process, one of which is the Weibull process. These point processes occur as failure-time models in the reliability theory of repairable systems.

Poisson theorem for non-homogeneous Markov chains

1989 ◽  
Vol 26 (03) ◽  
pp. 637-642 ◽  
Author(s):  
Janusz Pawłowski
Keyword(s):  
Markov Chains ◽  
Poisson Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Compound Poisson Distribution ◽  
Convergence In Distribution ◽  
Compound Poisson ◽  
Necessary And Sufficient

This paper gives necessary and sufficient conditions for the convergence in distribution of sums of the 0–1 Markov chains to a compound Poisson distribution.

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