Abstract:
Asymptotic expansions are widely used in studying properties of probabilities. One can mention in this connection papers by Cramйr, Richter, Petrov, Statulyavichus, Saulis, Franken, Kalinin, Bikyalis, Zhemaitis, and many others. Expansions of such a kind are constructed, as a rule, by means of semi-invariants in the case of continuous random variables (r.v.'s) and by means of factorial semi-invariants in the case of lattice r.v.'s. In this paper different expansions for the probabilities of sums of independent identically distributed lattice r.v.'s are considered. These expansions use other numerical characteristics, namely, the values of the derivatives of the logarithm of a generating function at point zero. The advantages of the method are discussed in detail.
Keywords:
sum of independent identically distributed lattice random variables, generating function, the value at point zero of the derivative of the logarithm of a generating function.
Citation:
Š. Jakševičius, “On a method of expansion of the probabilities of lattice random variables”, Teor. Veroyatnost. i Primenen., 42:2 (1997), 294–307; Theory Probab. Appl., 42:2 (1998), 271–282
Cekanavicius V., “Approximation Methods in Probability Theory”, Approximation Methods in Probability Theory, Universitext, Springer International Publishing Ag, 2016, 1–274
Vydas Čekanavičius, Universitext, Approximation Methods in Probability Theory, 2016, 223
Vydas Čekanavičius, Universitext, Approximation Methods in Probability Theory, 2016, 69
Vydas Čekanavičius, Universitext, Approximation Methods in Probability Theory, 2016, 51
Vydas Čekanavičius, Universitext, Approximation Methods in Probability Theory, 2016, 21
Vydas Čekanavičius, Universitext, Approximation Methods in Probability Theory, 2016, 207
D. N. Karymov, “On the decomposition of lattice distributions
into convolutions of Poisson signed measures”, Theory Probab. Appl., 49:3 (2005), 545–552
Citation in format AMSBIB
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