Estimating the mean of a heavy tailed distribution

DOI10.1016/S0167-7152(00)00203-0zbMath0981.62041OpenAlexW2079636387MaRDI QIDQ5937048

Liang Peng

Publication date: 26 March 2002

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

Full work available at URL: https://doi.org/10.1016/s0167-7152(00)00203-0

zbMATH Keywords

normal distributionheavy tailsstable lawtrimmed mean

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Point estimation (62F10) Statistics of extreme values; tail inference (62G32)

Related Items (20)

Empirical-likelihood-based confidence interval for the mean with a heavy-tailed distribution. ⋮ ESTIMATION AND INFERENCE FOR MOMENTS OF RATIOS WITH ROBUSTNESS AGAINST LARGE TRIMMING BIAS ⋮ ESTIMATION OF RISK MEASURES FROM HEAVY TAILED DISTRIBUTIONS ⋮ Estimating the Mean of Heavy-tailed Distribution under Random Truncation ⋮ Estimation of the Ruin Probability in Infinite Time for Heavy Right-Tailed Losses ⋮ A nonparametric sequential test with power 1 for the mean of Lévy-stable laws with infinite variance ⋮ Semi-parametric estimation of the quintile share ratio index of inequality measure for heavy-tailed income distributions with index in the upper half of the unit interval ⋮ A nonparametric repeated significance test with adaptive target sample size ⋮ Haezendonck-Goovaerts risk measure with a heavy tailed loss ⋮ Estimating the conditional tail expectation in the case of heavy-tailed losses ⋮ Estimating L-functionals for heavy-tailed distributions and application ⋮ Extreme Value Theory and Statistics of Univariate Extremes: A Review ⋮ GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference ⋮ Contrasting the Gini and Zenga indices of economic inequality ⋮ Estimating the distortion parameter of the proportional-hazard premium for heavy-tailed losses ⋮ Empirical estimation of the proportional hazard premium for heavy-tailed claim amounts ⋮ Heavy tailed capital incomes: Zenga index, statistical inference, and ECHP data analysis ⋮ Expected utility and catastrophic consumption risk ⋮ Point process-based Monte Carlo estimation ⋮ Estimating the scale parameter of a Lévy-stable distribution via the extreme value approach

Cites Work

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• What portion of the sample makes a partial sum asymptotically stable or normal?
• Weighted empirical and quantile processes
• The asymptotic distribution of trimmed sums
• A probabilistic approach to the asymptotic distribution of sums of independent, identically distributed random variables
• Laws of large numbers for sums of extreme values
• Asymptotic normality and subsequential limits of trimmed sums
• On bootstrap estimation of the distribution of the Studentized mean
• Central limit theorems for sums of extreme values

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