Asymptotic expansions for probability distributions
Asymptotic expansions of Grigelionis - Franken type are obtained in a local theorem for nonnegative integer-valued random variables \(X=X_{\Delta}[in\) spirit of \textit{V. A. Statulevičius}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 6, 133-144 (1966; Zbl 0158.362)]. The limit distribution is Poisson [see also \textit{A. Bikelis} and \textit{A. Žemaitis}, Litov. Mat. Sb. 16, No.3, 31-50 (1976; Zbl 0353.60033)]. The factorial cumulants of \(X_{\Delta}\) satisfy the Bernstein- Statulevičius type condition. A parameter allowing to vary the form of expansion is involved.
nonnegative integer-valued random variables
scientific article; zbMATH DE number 3852119