Limit theorems for the number and sum of near-maxima for medium tails.

DOI10.1016/S0167-7152(03)00085-3zbMath1116.60320OpenAlexW1985041815MaRDI QIDQ1423174

Chun Su, Zhishui Hu

Publication date: 14 February 2004

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-7152(03)00085-3

zbMATH Keywords

Exponential distributionMedium tailNear-maximaThick tail

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05) Strong limit theorems (60F15)

Related Items (17)

Asymptotic properties of numbers of observations near sample quantiles ⋮ Numbers of near-maxima for the bivariate case ⋮ Number of observations near the maximum in anF^α-scheme ⋮ Asymptotic normality of numbers of observations near order statistics from stationary processes ⋮ Limit laws for the cumulative number of ties for the maximum in a random sequence ⋮ Some bounds for the expectations of functions on order statistics and their applications ⋮ A limit theorem for random products of trimmed sums of i.i.d. random variables ⋮ Asymptotic properties of numbers of observations in random regions determined by central order statistics ⋮ On the number and sum of near-record observations ⋮ Asymptotic properties of numbers of near minimum observations under progressive type-II censoring ⋮ On the Asymptotic Behaviour of Extremes and Near Maxima of Random Observations from the General Error Distributions ⋮ Asymptotic normality of numbers of observations in random regions determined by order statistics ⋮ A note on the number of observations near an order statistic ⋮ How Many Observations Fall in a Neighborhood of an Order Statistic? ⋮ LIMIT THEOREMS FOR PROPORTIONS OF OBSERVATIONS FALLING INTO RANDOM REGIONS DETERMINED BY ORDER STATISTICS ⋮ NUMBERS OF OBSERVATIONS NEAR ORDER STATISTICS ⋮ The asymptotic distribution of numbers of observations near order statistics

Cites Work

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• The contribution to the sum of the summand of maximum modulus
• Limiting behavior of weighted sums of independent random variables
• A note on the number of records near the maximum
• Limit laws for the number of near maxima via the Poisson approximation
• The number and sum of near-maxima for thin-tailed populations
• ON THE NUMBER OF RECORDS NEAR THE MAXIMUM
• On the rate of growth of the overshoot and the maximum partial sum

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