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

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.

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On a stochastic process occurring in queueing systems

Journal of Applied Probability ◽

10.2307/3212208 ◽

1965 ◽

Vol 2 (2) ◽

pp. 467-469 ◽

Cited By ~ 1

Author(s):

U. N. Bhat

Keyword(s):

Stochastic Process ◽

Poisson Distribution ◽

Waiting Time ◽

Queueing Systems ◽

Distribution Functions ◽

Compound Poisson Distribution ◽

Compound Poisson ◽

Transition Distribution

SummaryTransition distribution functions (d.f.) of the stochastic process u + t − X(t), where X(t) has a compound Poisson distribution, are used to derive explicit results for the transition d.f.s of the waiting time processes in the queueing systems M/G/1 and GI/M/1.

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

Journal of Applied Probability ◽

10.1017/s0021900200111830 ◽

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.

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On a stochastic process occurring in queueing systems

Journal of Applied Probability ◽

10.1017/s0021900200108794 ◽

1965 ◽

Vol 2 (02) ◽

pp. 467-469

Author(s):

U. N. Bhat

Keyword(s):

Stochastic Process ◽

Poisson Distribution ◽

Waiting Time ◽

Queueing Systems ◽

Distribution Functions ◽

Compound Poisson Distribution ◽

Compound Poisson ◽

Transition Distribution

Summary Transition distribution functions (d.f.) of the stochastic process u + t − X(t), where X(t) has a compound Poisson distribution, are used to derive explicit results for the transition d.f.s of the waiting time processes in the queueing systems M/G/1 and GI/M/1.

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

Journal of Applied Probability ◽

10.2307/3214006 ◽

1986 ◽

Vol 23 (3) ◽

pp. 679-687 ◽

Cited By ~ 2

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.

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The compound Poisson distribution of the number of matches of values of a discrete function of s-tuples in segments of a sequence of random variables

Discrete Mathematics and Applications ◽

10.1515/dma.2007.017 ◽

2007 ◽

Vol 17 (3) ◽

Author(s):

A. M. Shoitov

Keyword(s):

Poisson Distribution ◽

Random Variables ◽

Compound Poisson Distribution ◽

Discrete Function ◽

Compound Poisson

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Log-Compound-Poisson Distribution Model of Intermittency in Turbulence

Zeitschrift für Naturforschung A ◽

10.1515/zna-1998-10-1105 ◽

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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