Asymptotic expansions for the probabilities of large deviations. Normal approximation. III

1976 ◽  
Vol 16 (3) ◽  
pp. 332-348 ◽  
Author(s):  
A. Bikelis ◽  
A. Žemaitis
Keyword(s):  
Large Deviations ◽  
Asymptotic Expansions ◽  
Normal Approximation ◽  
Probabilities Of Large Deviations

scholarly journals Asymptotic expansions for the probabilities of large deviations for sums of random variables related to a Markov chain

1970 ◽  
Vol 10 (2) ◽  
pp. 359-366
Author(s):  
L. Saulis ◽  
V. Statulevičius
Keyword(s):  
Markov Chain ◽  
Large Deviations ◽  
Asymptotic Expansions ◽  
Random Variables ◽  
Sums Of Random Variables ◽  
Probabilities Of Large Deviations

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Л. И. Саулис, В. А. Статулявичус. Асимптотическое разложение для вероятностей больших уклонений сумм случайных величин, связанных в цепь Маркова L. Saulis, V. Statulevičius. Atsitiktinių dydžių, surištų į Markovo grandinę, didžiųjų nukrypimų asimptotinis dėstinys

scholarly journals On the asymptotic expansions for the probabilities of large deviations

1969 ◽  
Vol 9 (3) ◽  
pp. 605-625
Author(s):  
L. Saulis
Keyword(s):  
Large Deviations ◽  
Asymptotic Expansions ◽  
Probabilities Of Large Deviations

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Л. Саулис. Асимптотическое разложение для вероятностей больших уклонений L. Saulis. Didelių nukrypimų tikimybių asimptotinis išdėstymas

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.

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