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Sample Sequences of Maxima
- Source :
- Ann. Math. Statist. 38, no. 5 (1967), 1570-1574
- Publication Year :
- 1967
- Publisher :
- The Institute of Mathematical Statistics, 1967.
-
Abstract
- Let $X_1, X_2, \cdots, X_n, \cdots$ be a sequence of independent, identically distributed random variables with common distribution function $F$. Let $Z_n = \max \{X_1, X_2, \cdots X_n\}$. Conditions for the stability and relative stability of such sequences with the various modes of convergence have been given by Geffroy [3], and Barndorff-Nielsen [1]. The principal result of this paper is Theorem 2.1, which is an analogue for maxima of the law of the iterated logarithm for sums (Loeve [6] pages 260-1). In Section 3, it is indicated that the theorem is satisfied by a wide class of distributions, and specific forms are given for the normal and exponential distributions.
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Ann. Math. Statist. 38, no. 5 (1967), 1570-1574
- Accession number :
- edsair.doi.dedup.....2d6c6e92d03baf59f19cfb65f51163a7