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.

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.

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.

Poisson theorem for non-homogeneous Markov chains

1989 ◽  
Vol 26 (3) ◽  
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.

scholarly journals Approximations for sums of three-valued 1-dependent symmetric random variables

2020 ◽  
Vol 25 (4) ◽  
Author(s):  
Gabija Liaudanskaitė ◽  
Vydas Čekanavičius
Keyword(s):  
Total Variation ◽  
Poisson Distribution ◽  
Random Variables ◽  
Distribution Functions ◽  
Compound Poisson Distribution ◽  
Compound Poisson ◽  
Triangular Arrays ◽  
Uniformly Bounded ◽  
Accuracy Of Approximation

The sum of symmetric three-point 1-dependent nonidentically distributed random variables is approximated by a compound Poisson distribution. The accuracy of approximation is estimated in the local and total variation norms. For distributions uniformly bounded from zero,the accuracy of approximation is of the order O(n–1). In the general case of triangular arrays of identically distributed summands, the accuracy is at least of the order O(n–1/2). Nonuniform estimates are obtained for distribution functions and probabilities. The characteristic functionmethod is used.  

Log-Compound-Poisson Distribution Model of Intermittency in Turbulence

1998 ◽  
Vol 53 (10-11) ◽  
pp. 828-832
Author(s):  
Feng Quing-Zeng
Keyword(s):  
Energy Dissipation ◽  
Poisson Distribution ◽  
Turbulent Energy ◽  
Compound Poisson Distribution ◽  
Distribution Model ◽  
Velocity Difference ◽  
Scaling Exponents ◽  
Compound Poisson ◽  
Developed Turbulence ◽  
Experimental Values

Abstract The log-compound-Poisson distribution for the breakdown coefficients of turbulent energy dissipation is proposed, and the scaling exponents for the velocity difference moments in fully developed turbulence are obtained, which agree well with experimental values up to measurable orders. The under-lying physics of this model is directly related to the burst phenomenon in turbulence, and a detailed discussion is given in the last section.

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