Some approximation methods for the distribution of random sums

DOI10.1016/0167-6687(83)90024-0zbMath0519.62014OpenAlexW2048215874MaRDI QIDQ1054403

G. Rappl, Rainer von Chossy

Publication date: 1983

Published in: Insurance Mathematics \& Economics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-6687(83)90024-0

zbMATH Keywords

central limit theoremEdgeworth expansionBerry-Esseen theoremcompound Poisson distributiondistribution of random sumsEsscher approximation

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Applications of statistics to actuarial sciences and financial mathematics (62P05) Central limit and other weak theorems (60F05)

Related Items (11)

Sharp orders of convergence in the random central limit theorem ⋮ COMPARISON OF APPROXIMATIONS FOR COMPOUND POISSON PROCESSES ⋮ Sharpened upper bounds for the absolute constant in the Berry-Esseen inequality for mixed Poisson random sums ⋮ \(L_1\) bounds for asymptotic normality of random sums of independent random variables ⋮ On the normal approximation of a sum of a random number of independent random variables ⋮ On the normal approximation of a binomial random sum ⋮ Some estimates of normal approximation for the distribution of a sum of a random number of independent random variables ⋮ Asymptotic expansions in the central limit theorem for compound and Markov processes ⋮ On the computation of aggregate claims distributions: some new approximations ⋮ An improvement of the Berry–Esseen inequality with applications to Poisson and mixed Poisson random sums ⋮ On the normal approximation of a negative binomial random sum

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