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Rolling Extended Stats: sem, skew, kurt, quantile

Higher-order rolling window statistics extending the core pandas.Series.rolling() API: sem, skew, kurt, and quantile.

1. rollingSem — Standard Error of the Mean

The standard error of the mean measures how much the sample mean would vary across repeated samples. For a window of n values:

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1. rollingSem — Standard Error of the Mean

The standard error of the mean measures how much the sample mean would vary across repeated samples. For a window of n values:

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2. rollingSkew — Fisher-Pearson Skewness

Skewness measures asymmetry of the distribution in each window. Positive = right tail heavier; negative = left tail heavier. Uses the unbiased Fisher-Pearson formula (same as pandas):

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2. rollingSkew — Fisher-Pearson Skewness

Skewness measures asymmetry of the distribution in each window. Positive = right tail heavier; negative = left tail heavier. Uses the unbiased Fisher-Pearson formula (same as pandas):

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3. rollingKurt — Excess Kurtosis

Kurtosis measures how heavy the tails are relative to a normal distribution. The excess kurtosis subtracts 3, so a normal distribution gives 0. Uses the Fisher (1930) unbiased formula:

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3. rollingKurt — Excess Kurtosis

Kurtosis measures how heavy the tails are relative to a normal distribution. The excess kurtosis subtracts 3, so a normal distribution gives 0. Uses the Fisher (1930) unbiased formula:

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4. rollingQuantile — Rolling Quantile

Computes any quantile within each sliding window using configurable interpolation. When q = 0.5 this is identical to rolling.median().

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