Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted skewness and kurtosis unbiased by sample size   Central moments and cumulants are often employed to characterize the
distribution of data. The skewness and kurtosis are particularly useful for the
detection of outliers, the assessment of departures from normally distributed
data, automated classification techniques and other applications. Robust
definitions of higher order moments are more stable but might miss
characteristic features of the data, as in the case of astronomical time series
with rare events like stellar bursts or eclipses from binary systems. Weighting
can help identify reliable measurements from uncertain or spurious outliers, so
unbiased estimates of the weighted skewness and kurtosis moments and cumulants,
corrected for sample-size biases, are provided under the assumption of
independent data. The comparison of biased and unbiased weighted estimators is
illustrated with simulations as a function of sample size, employing different
data distributions and weighting schemes.

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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg