Abstract
Let X 1, X 2,... be a sequence of nonnegative independent, identically distributed random variables and write S n =X 1+X 2+...+X n and M n =max (X 1, X 2, ..., X n ) for every n≥1. Let N be a nonnegative integer valued random variable, independent of X 1, X 2, .... We investigate in which way the asymptomic behaviour of P(S n ≤x)−P(M n ≤x) as x→∞ is preserved when n is replaced by N.
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Omey, E., Willekens, E. (1987). On the difference between distributions of sums and maxima. In: Kalashnikov, V.V., Penkov, B., Zolotarev, V.M. (eds) Stability Problems for Stochastic Models. Lecture Notes in Mathematics, vol 1233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072716
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DOI: https://doi.org/10.1007/BFb0072716
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