scholarly journals Log-concavity, ultra-log-concavity, and a maximum entropy property of discrete compound Poisson measures

2013 ◽  
Vol 161 (9) ◽  
pp. 1232-1250 ◽  
Author(s):  
Oliver Johnson ◽  
Ioannis Kontoyiannis ◽  
Mokshay Madiman
Keyword(s):  
Maximum Entropy ◽  
Compound Poisson ◽  
Poisson Measures

Asymptotic Expansions in the Exponent: a Compound Poisson Approach

1997 ◽  
Vol 29 (02) ◽  
pp. 374-387 ◽  
Author(s):  
V. Čekanavičius
Keyword(s):  
Asymptotic Expansion ◽  
Large Deviations ◽  
Poisson Distribution ◽  
Asymptotic Expansions ◽  
Compound Poisson ◽  
Poisson Measures ◽  
Poisson Approximations

The accuracy of the Normal or Poisson approximations can be significantly improved by adding part of an asymptotic expansion in the exponent. The signed-compound-Poisson measures obtained in this manner can be of the same structure as the Poisson distribution. For large deviations we prove that signed-compound-Poisson measures enlarge the zone of equivalence for tails.

Asymptotic Expansions in the Exponent: a Compound Poisson Approach

1997 ◽  
Vol 29 (2) ◽  
pp. 374-387 ◽  
Author(s):  
V. Čekanavičius
Keyword(s):  
Asymptotic Expansion ◽  
Large Deviations ◽  
Poisson Distribution ◽  
Asymptotic Expansions ◽  
Compound Poisson ◽  
Poisson Measures ◽  
Poisson Approximations

The accuracy of the Normal or Poisson approximations can be significantly improved by adding part of an asymptotic expansion in the exponent. The signed-compound-Poisson measures obtained in this manner can be of the same structure as the Poisson distribution. For large deviations we prove that signed-compound-Poisson measures enlarge the zone of equivalence for tails.

Infinitely divisible approximations for discrete nonlattice variables

2003 ◽  
Vol 35 (04) ◽  
pp. 982-1006
Author(s):  
V. Čekanavičius
Keyword(s):  
Asymptotic Expansions ◽  
Random Variables ◽  
Second Order ◽  
Independent Random Variables ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Compound Poisson ◽  
Set Of Points ◽  
Poisson Measures

Sums of independent random variables concentrated on discrete, not necessarily lattice, set of points are approximated by infinitely divisible distributions and signed compound Poisson measures. A version of Kolmogorov's first uniform theorem is proved. Second-order asymptotic expansions are constructed for distributions with pseudo-lattice supports.

scholarly journals The Jackson Queueing Network Model Built Using Poisson Measures. Application To A Bank Model

2014 ◽  
Vol 13 (2) ◽  
pp. 7-22
Author(s):  
Daniel Ciuiu
Keyword(s):  
Network Model ◽  
Queueing Networks ◽  
Queueing Network ◽  
Poisson Processes ◽  
External Shocks ◽  
Exponential Distributions ◽  
Compound Poisson ◽  
Deposit Type ◽  
The Relationship ◽  
Poisson Measures

Abstract In this paper we will build a bank model using Poisson measures and Jackson queueing networks. We take into account the relationship between the Poisson and the exponential distributions, and we consider for each credit/deposit type a node where shocks are modeled as the compound Poisson processes. The transmissions of the shocks are modeled as moving between nodes in Jackson queueing networks, the external shocks are modeled as external arrivals, and the absorption of shocks as departures from the network.

Infinitely divisible approximations for discrete nonlattice variables

2003 ◽  
Vol 35 (4) ◽  
pp. 982-1006 ◽  
Author(s):  
V. Čekanavičius
Keyword(s):  
Asymptotic Expansions ◽  
Random Variables ◽  
Second Order ◽  
Independent Random Variables ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Compound Poisson ◽  
Set Of Points ◽  
Poisson Measures

Sums of independent random variables concentrated on discrete, not necessarily lattice, set of points are approximated by infinitely divisible distributions and signed compound Poisson measures. A version of Kolmogorov's first uniform theorem is proved. Second-order asymptotic expansions are constructed for distributions with pseudo-lattice supports.

Compound Poisson approximations for sums of discrete nonlattice variables

2003 ◽  
Vol 35 (1) ◽  
pp. 228-250 ◽  
Author(s):  
V. Čekanavičius ◽  
Y. H. Wang
Keyword(s):  
Normal Distribution ◽  
Asymptotic Expansions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Compound Poisson ◽  
Poisson Distributions ◽  
Set Of Points ◽  
Poisson Measures ◽  
Poisson Approximations

Sums of independent random variables concentrated on the same finite discrete, not necessarily lattice, set of points are approximated by compound Poisson distributions and signed compound Poisson measures. Such approximations can be more accurate than the normal distribution. Short asymptotic expansions are constructed.

Compound Poisson approximations for sums of discrete nonlattice variables

2003 ◽  
Vol 35 (01) ◽  
pp. 228-250 ◽  
Author(s):  
V. Čekanavičius ◽  
Y. H. Wang
Keyword(s):  
Normal Distribution ◽  
Asymptotic Expansions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Compound Poisson ◽  
Poisson Distributions ◽  
Set Of Points ◽  
Poisson Measures ◽  
Poisson Approximations

Sums of independent random variables concentrated on the same finite discrete, not necessarily lattice, set of points are approximated by compound Poisson distributions and signed compound Poisson measures. Such approximations can be more accurate than the normal distribution. Short asymptotic expansions are constructed.

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