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Article
Necessary conditions for characterization of laws via mixed sums
SupposeX andY are independent and identically distributed, and independent ofU which satisfies 0≤U≤1. Recent work has centered on finding the lawsL(X) for whichX ℞U(X+Y) where ℞ denotes equality in law. We show t...
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Article
Criteria for Convergence of the Number of Near Maxima for Long Tails
Let M n denote the maximum of a random sample of size n and K n (a) be the number of near maxima, i.e. the number of sample observations in the...
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Article
Limit theorems for numbers of near-records
Observations occurring between successive record times and within a distance a > 0 of the current record value are called near-records. Limit theorems for the number ξ n
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Article
Limit theorems for record counts and times in the F α -scheme
We determine the almost sure and central limiting behaviour of the number of records and record times for the F α -scheme. Elementary methods are used to obtain ...
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Article
On relative stability and weighted laws of large numbers
Weighted laws of large numbers are established for components which are independent copies of a positive relatively stable law and the weights comprise a regularly varying sequence. The index of regular variat...