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- W3105420202 abstract "Here we suppose that the observed random variable has cumulative distribution function $F$ with regularly varying tail, i.e. $1-F in RV_{-alpha}$, $alpha > 0$. Using the results about exponential order statistics we investigate logarithms of ratios of two order statistics of a sample of independent observations on Pareto distributed random variable with parameter $alpha$. Short explicit formulae for its mean and variance are obtained. Then we transform this function in such a way that to obtain unbiased, asymptotically efficient, and asymptotically normal estimator for $alpha$. Finally we simulate Pareto samples and show that in the considered cases the proposed estimator outperforms the well known Hill, t-Hill, Pickands and Deckers-Einmahl-de Haan estimators." @default.
- W3105420202 created "2020-11-23" @default.
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- W3105420202 date "2019-01-01" @default.
- W3105420202 modified "2023-09-23" @default.
- W3105420202 title "Logarithm of ratios of two order statistics and regularly varying tails" @default.
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- W3105420202 doi "https://doi.org/10.1063/1.5130791" @default.
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