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Descriptive Statistics#

statista.time_series.descriptive #

Descriptive statistics for TimeSeries.

This module provides the Descriptive class which adds statistical summary properties and methods to TimeSeries. It includes conventional moments (mean, std, skewness, kurtosis), robust measures (MAD, IQR), and L-moments for distribution identification.

Descriptive #

Bases: _TimeSeriesStub

Descriptive statistical methods for TimeSeries.

Source code in src\statista\time_series\descriptive.py 
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class Descriptive(_TimeSeriesStub):
    """Descriptive statistical methods for TimeSeries."""

    @property
    def stats(self) -> DataFrame:
        """Basic statistical summary of the time series.

        Delegates to ``pandas.DataFrame.describe()``, returning count, mean,
        standard deviation, min, quartiles, and max for each column.

        Returns:
            pandas.DataFrame:
                One column per series. Rows: count, mean, std, min, 25%, 50%, 75%, max.

        Examples:
            - Load real hydrological data and inspect basic statistics:
                ```python
                >>> import numpy as np
                >>> from statista.time_series import TimeSeries
                >>> data = np.loadtxt("examples/data/time_series1.txt")
                >>> ts = TimeSeries(data)
                >>> s = ts.stats
                >>> s.index.tolist()
                ['count', 'mean', 'std', 'min', '25%', '50%', '75%', 'max']
                >>> round(float(s.loc["mean", "Series1"]), 2)
                16.93

                ```
            - Multi-column data returns one column per series:
                ```python
                >>> import numpy as np
                >>> from statista.time_series import TimeSeries
                >>> np.random.seed(42)
                >>> ts = TimeSeries(np.random.randn(100, 2), columns=["A", "B"])
                >>> s = ts.stats
                >>> s.columns.tolist()
                ['A', 'B']
                >>> int(s.loc["count", "A"])
                100

                ```

        See Also:
            extended_stats: Adds CV, skewness, kurtosis, IQR, MAD, and extra percentiles.
            summary: Paper-ready table combining extended_stats and L-moment ratios.
        """
        return self.describe()

    @property
    def extended_stats(self) -> DataFrame:
        """Comprehensive statistical summary with 17 measures per column.

        Extends ``stats`` with coefficient of variation (CV), skewness (bias-corrected),
        excess kurtosis (bias-corrected), additional percentiles (5%, 10%, 90%, 95%),
        interquartile range (IQR), and median absolute deviation (MAD). NaN values are
        dropped per column before computation.

        Returns:
            pandas.DataFrame:
                One column per series. Rows: count, mean, std, cv, skewness, kurtosis,
                min, 5%, 10%, 25%, 50%, 75%, 90%, 95%, max, iqr, mad.

        Examples:
            - Compute extended statistics for real hydrological data:
                ```python
                >>> import numpy as np
                >>> from statista.time_series import TimeSeries
                >>> data = np.loadtxt("examples/data/time_series1.txt")
                >>> ts = TimeSeries(data)
                >>> e = ts.extended_stats
                >>> e.index.tolist()
                ['count', 'mean', 'std', 'cv', 'skewness', 'kurtosis', 'min', '5%', '10%', '25%', '50%', '75%', '90%', '95%', 'max', 'iqr', 'mad']
                >>> round(float(e.loc["cv", "Series1"]), 4)
                0.0615
                >>> round(float(e.loc["skewness", "Series1"]), 4)
                0.9279

                ```
            - Multi-column with named columns:
                ```python
                >>> import numpy as np
                >>> from statista.time_series import TimeSeries
                >>> np.random.seed(42)
                >>> data = np.column_stack([np.random.randn(100) * 10 + 50,
                ...                         np.random.randn(100) * 5 + 20])
                >>> ts = TimeSeries(data, columns=["Flow", "Temp"])
                >>> e = ts.extended_stats
                >>> round(float(e.loc["mean", "Flow"]), 2)
                48.96
                >>> round(float(e.loc["mean", "Temp"]), 2)
                20.11

                ```
            - NaN values are excluded from calculations:
                ```python
                >>> import numpy as np
                >>> from statista.time_series import TimeSeries
                >>> data = np.array([1.0, 2.0, np.nan, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0])
                >>> ts = TimeSeries(data)
                >>> e = ts.extended_stats
                >>> int(e.loc["count", "Series1"])
                9
                >>> round(float(e.loc["mean", "Series1"]), 4)
                5.7778

                ```

        See Also:
            stats: Basic 8-row summary via pandas describe().
            l_moments: L-moment ratios for robust distribution identification.
            summary: Combined table of extended_stats + L-moment ratios.
        """
        stat_names = [
            "count",
            "mean",
            "std",
            "cv",
            "skewness",
            "kurtosis",
            "min",
            "5%",
            "10%",
            "25%",
            "50%",
            "75%",
            "90%",
            "95%",
            "max",
            "iqr",
            "mad",
        ]
        result = DataFrame(index=stat_names, columns=self.columns, dtype=float)

        for col in self.columns:
            data = self[col].dropna().values
            n = len(data)
            mean = np.mean(data)
            std = np.std(data, ddof=1)
            quantiles = np.percentile(data, [5, 10, 25, 50, 75, 90, 95])
            q25, q75 = quantiles[2], quantiles[4]

            result.loc["count", col] = n
            result.loc["mean", col] = mean
            result.loc["std", col] = std
            result.loc["cv", col] = std / mean if not np.isclose(mean, 0.0) else np.nan
            result.loc["skewness", col] = skew(data, bias=False)
            result.loc["kurtosis", col] = scipy_kurtosis(data, bias=False)
            result.loc["min", col] = np.min(data)
            result.loc["5%", col] = quantiles[0]
            result.loc["10%", col] = quantiles[1]
            result.loc["25%", col] = q25
            result.loc["50%", col] = quantiles[3]
            result.loc["75%", col] = q75
            result.loc["90%", col] = quantiles[5]
            result.loc["95%", col] = quantiles[6]
            result.loc["max", col] = np.max(data)
            result.loc["iqr", col] = q75 - q25
            result.loc["mad", col] = median_abs_deviation(data)

        return result

    def l_moments(self, nmom: int = 5) -> DataFrame:
        """Compute sample L-moments and L-moment ratios for each column.

        L-moments (Hosking, 1990) are summary statistics computed from linear
        combinations of order statistics. They are more robust to outliers than
        conventional moments and better suited for small samples and heavy-tailed
        data. They are the standard tool for distribution identification in
        regional frequency analysis.

        Args:
            nmom: Number of L-moments to compute. Must be >= 2. Default is 5.

        Returns:
            pandas.DataFrame:
                Rows: L1 (L-location = mean), L2 (L-scale), t (L-CV = L2/L1),
                t3 (L-skewness = L3/L2), t4 (L-kurtosis = L4/L2), and
                optionally t5 if nmom >= 5. One column per series.

        Raises:
            ValueError: If nmom < 2.

        Examples:
            - Compute L-moments for real hydrological data:
                ```python
                >>> import numpy as np
                >>> from statista.time_series import TimeSeries
                >>> data = np.loadtxt("examples/data/time_series1.txt")
                >>> ts = TimeSeries(data)
                >>> lm = ts.l_moments(nmom=4)
                >>> lm.index.tolist()
                ['L1', 'L2', 't', 't3', 't4']
                >>> round(float(lm.loc["L1", "Series1"]), 4)
                16.9292
                >>> round(float(lm.loc["t3", "Series1"]), 4)
                0.4815

                ```
            - L1 equals the sample mean:
                ```python
                >>> import numpy as np
                >>> from statista.time_series import TimeSeries
                >>> data = np.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0])
                >>> ts = TimeSeries(data)
                >>> lm = ts.l_moments(nmom=2)
                >>> lm.index.tolist()
                ['L1', 'L2', 't']
                >>> float(lm.loc["L1", "Series1"])
                5.5

                ```
            - Symmetric data has L-skewness near zero:
                ```python
                >>> import numpy as np
                >>> from statista.time_series import TimeSeries
                >>> data = np.array([-5., -4., -3., -2., -1., 0., 1., 2., 3., 4., 5.])
                >>> ts = TimeSeries(data)
                >>> lm = ts.l_moments(nmom=4)
                >>> round(float(lm.loc["t3", "Series1"]), 4)
                0.0

                ```

        References:
            Hosking, J.R.M. (1990). L-moments: Analysis and estimation of
            distributions using linear combinations of order statistics. Journal
            of the Royal Statistical Society, Series B, 52(1), 105-124.

        See Also:
            extended_stats: Conventional moments (skewness, kurtosis) and percentiles.
            summary: Combined table of extended_stats + L-moment ratios.
        """
        if nmom < 2:
            raise ValueError("nmom must be >= 2")

        row_names = ["L1", "L2"]
        if nmom >= 2:
            row_names.append("t")
        if nmom >= 3:
            row_names.append("t3")
        if nmom >= 4:
            row_names.append("t4")
        if nmom >= 5:
            row_names.append("t5")

        result = DataFrame(index=row_names, columns=self.columns, dtype=float)

        for col in self.columns:
            data = self[col].dropna().values
            lmom_calc = Lmoments(data)
            lmoms = lmom_calc.calculate(nmom=nmom)

            l1 = lmoms[0]
            l2 = lmoms[1]
            result.loc["L1", col] = l1
            result.loc["L2", col] = l2
            result.loc["t", col] = l2 / l1 if not np.isclose(l1, 0.0) else np.nan
            if nmom >= 3:
                result.loc["t3", col] = (
                    lmoms[2] / l2 if not np.isclose(l2, 0.0) else np.nan
                )
            if nmom >= 4:
                result.loc["t4", col] = (
                    lmoms[3] / l2 if not np.isclose(l2, 0.0) else np.nan
                )
            if nmom >= 5:
                result.loc["t5", col] = (
                    lmoms[4] / l2 if not np.isclose(l2, 0.0) else np.nan
                )

        return result

    def summary(self) -> DataFrame:
        """Comprehensive summary table suitable for a research paper.

        Combines ``extended_stats`` and ``l_moments`` into a single table with
        13 rows per column. This produces the kind of "Table 1" that goes into
        a paper's methods or study-area section.

        Returns:
            pandas.DataFrame:
                One column per series. Rows: count, mean, std, cv, skewness,
                kurtosis, min, max, iqr, mad, L-CV, L-skewness, L-kurtosis.

        Examples:
            - Generate a paper-ready summary from real data:
                ```python
                >>> import numpy as np
                >>> from statista.time_series import TimeSeries
                >>> data = np.loadtxt("examples/data/time_series1.txt")
                >>> ts = TimeSeries(data)
                >>> sm = ts.summary()
                >>> sm.index.tolist()
                ['count', 'mean', 'std', 'cv', 'skewness', 'kurtosis', 'min', 'max', 'iqr', 'mad', 'L-CV', 'L-skewness', 'L-kurtosis']
                >>> len(sm)
                13
                >>> round(float(sm.loc["L-skewness", "Series1"]), 4)
                0.4815

                ```
            - Multi-column summary for comparing stations:
                ```python
                >>> import numpy as np
                >>> from statista.time_series import TimeSeries
                >>> np.random.seed(42)
                >>> data = np.column_stack([np.random.randn(100) * 10 + 50,
                ...                         np.random.randn(100) * 5 + 20])
                >>> ts = TimeSeries(data, columns=["Flow", "Temp"])
                >>> sm = ts.summary()
                >>> sm.columns.tolist()
                ['Flow', 'Temp']
                >>> round(float(sm.loc["mean", "Flow"]), 2)
                48.96

                ```

        See Also:
            extended_stats: The 17-row conventional statistics table.
            l_moments: L-moment ratios independently.
        """
        estats = self.extended_stats
        lmom = self.l_moments(nmom=4)

        summary_rows = [
            "count",
            "mean",
            "std",
            "cv",
            "skewness",
            "kurtosis",
            "min",
            "max",
            "iqr",
            "mad",
        ]
        result = estats.loc[summary_rows, :].copy()

        result.loc["L-CV"] = lmom.loc["t"]
        result.loc["L-skewness"] = lmom.loc["t3"]
        result.loc["L-kurtosis"] = lmom.loc["t4"]

        return result
stats property #

Basic statistical summary of the time series.

Delegates to pandas.DataFrame.describe(), returning count, mean, standard deviation, min, quartiles, and max for each column.

Returns:

Type Description
DataFrame

pandas.DataFrame: One column per series. Rows: count, mean, std, min, 25%, 50%, 75%, max.

Examples:

  • Load real hydrological data and inspect basic statistics: 
    >>> import numpy as np
>>> from statista.time_series import TimeSeries
>>> data = np.loadtxt("examples/data/time_series1.txt")
>>> ts = TimeSeries(data)
>>> s = ts.stats
>>> s.index.tolist()
['count', 'mean', 'std', 'min', '25%', '50%', '75%', 'max']
>>> round(float(s.loc["mean", "Series1"]), 2)
16.93
  • Multi-column data returns one column per series: 
    >>> import numpy as np
>>> from statista.time_series import TimeSeries
>>> np.random.seed(42)
>>> ts = TimeSeries(np.random.randn(100, 2), columns=["A", "B"])
>>> s = ts.stats
>>> s.columns.tolist()
['A', 'B']
>>> int(s.loc["count", "A"])
100
See Also

extended_stats: Adds CV, skewness, kurtosis, IQR, MAD, and extra percentiles. summary: Paper-ready table combining extended_stats and L-moment ratios.

extended_stats property #

Comprehensive statistical summary with 17 measures per column.

Extends stats with coefficient of variation (CV), skewness (bias-corrected), excess kurtosis (bias-corrected), additional percentiles (5%, 10%, 90%, 95%), interquartile range (IQR), and median absolute deviation (MAD). NaN values are dropped per column before computation.

Returns:

Type Description
DataFrame

pandas.DataFrame: One column per series. Rows: count, mean, std, cv, skewness, kurtosis, min, 5%, 10%, 25%, 50%, 75%, 90%, 95%, max, iqr, mad.

Examples:

  • Compute extended statistics for real hydrological data: 
    >>> import numpy as np
>>> from statista.time_series import TimeSeries
>>> data = np.loadtxt("examples/data/time_series1.txt")
>>> ts = TimeSeries(data)
>>> e = ts.extended_stats
>>> e.index.tolist()
['count', 'mean', 'std', 'cv', 'skewness', 'kurtosis', 'min', '5%', '10%', '25%', '50%', '75%', '90%', '95%', 'max', 'iqr', 'mad']
>>> round(float(e.loc["cv", "Series1"]), 4)
0.0615
>>> round(float(e.loc["skewness", "Series1"]), 4)
0.9279
  • Multi-column with named columns: 
    >>> import numpy as np
>>> from statista.time_series import TimeSeries
>>> np.random.seed(42)
>>> data = np.column_stack([np.random.randn(100) * 10 + 50,
...                         np.random.randn(100) * 5 + 20])
>>> ts = TimeSeries(data, columns=["Flow", "Temp"])
>>> e = ts.extended_stats
>>> round(float(e.loc["mean", "Flow"]), 2)
48.96
>>> round(float(e.loc["mean", "Temp"]), 2)
20.11
  • NaN values are excluded from calculations: 
    >>> import numpy as np
>>> from statista.time_series import TimeSeries
>>> data = np.array([1.0, 2.0, np.nan, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0])
>>> ts = TimeSeries(data)
>>> e = ts.extended_stats
>>> int(e.loc["count", "Series1"])
9
>>> round(float(e.loc["mean", "Series1"]), 4)
5.7778
See Also

stats: Basic 8-row summary via pandas describe(). l_moments: L-moment ratios for robust distribution identification. summary: Combined table of extended_stats + L-moment ratios.

l_moments(nmom=5) #

Compute sample L-moments and L-moment ratios for each column.

L-moments (Hosking, 1990) are summary statistics computed from linear combinations of order statistics. They are more robust to outliers than conventional moments and better suited for small samples and heavy-tailed data. They are the standard tool for distribution identification in regional frequency analysis.

Parameters:

Name Type Description Default
nmom int

Number of L-moments to compute. Must be >= 2. Default is 5.

 5

Returns:

Type Description
DataFrame

pandas.DataFrame: Rows: L1 (L-location = mean), L2 (L-scale), t (L-CV = L2/L1), t3 (L-skewness = L3/L2), t4 (L-kurtosis = L4/L2), and optionally t5 if nmom >= 5. One column per series.

Raises:

Type Description
ValueError

If nmom < 2.

Examples:

  • Compute L-moments for real hydrological data: 
    >>> import numpy as np
>>> from statista.time_series import TimeSeries
>>> data = np.loadtxt("examples/data/time_series1.txt")
>>> ts = TimeSeries(data)
>>> lm = ts.l_moments(nmom=4)
>>> lm.index.tolist()
['L1', 'L2', 't', 't3', 't4']
>>> round(float(lm.loc["L1", "Series1"]), 4)
16.9292
>>> round(float(lm.loc["t3", "Series1"]), 4)
0.4815
  • L1 equals the sample mean: 
    >>> import numpy as np
>>> from statista.time_series import TimeSeries
>>> data = np.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0])
>>> ts = TimeSeries(data)
>>> lm = ts.l_moments(nmom=2)
>>> lm.index.tolist()
['L1', 'L2', 't']
>>> float(lm.loc["L1", "Series1"])
5.5
  • Symmetric data has L-skewness near zero: 
    >>> import numpy as np
>>> from statista.time_series import TimeSeries
>>> data = np.array([-5., -4., -3., -2., -1., 0., 1., 2., 3., 4., 5.])
>>> ts = TimeSeries(data)
>>> lm = ts.l_moments(nmom=4)
>>> round(float(lm.loc["t3", "Series1"]), 4)
0.0
References

Hosking, J.R.M. (1990). L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society, Series B, 52(1), 105-124.

See Also

extended_stats: Conventional moments (skewness, kurtosis) and percentiles. summary: Combined table of extended_stats + L-moment ratios.

Source code in src\statista\time_series\descriptive.py 
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def l_moments(self, nmom: int = 5) -> DataFrame:
    """Compute sample L-moments and L-moment ratios for each column.

    L-moments (Hosking, 1990) are summary statistics computed from linear
    combinations of order statistics. They are more robust to outliers than
    conventional moments and better suited for small samples and heavy-tailed
    data. They are the standard tool for distribution identification in
    regional frequency analysis.

    Args:
        nmom: Number of L-moments to compute. Must be >= 2. Default is 5.

    Returns:
        pandas.DataFrame:
            Rows: L1 (L-location = mean), L2 (L-scale), t (L-CV = L2/L1),
            t3 (L-skewness = L3/L2), t4 (L-kurtosis = L4/L2), and
            optionally t5 if nmom >= 5. One column per series.

    Raises:
        ValueError: If nmom < 2.

    Examples:
        - Compute L-moments for real hydrological data:
            ```python
            >>> import numpy as np
            >>> from statista.time_series import TimeSeries
            >>> data = np.loadtxt("examples/data/time_series1.txt")
            >>> ts = TimeSeries(data)
            >>> lm = ts.l_moments(nmom=4)
            >>> lm.index.tolist()
            ['L1', 'L2', 't', 't3', 't4']
            >>> round(float(lm.loc["L1", "Series1"]), 4)
            16.9292
            >>> round(float(lm.loc["t3", "Series1"]), 4)
            0.4815

            ```
        - L1 equals the sample mean:
            ```python
            >>> import numpy as np
            >>> from statista.time_series import TimeSeries
            >>> data = np.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0])
            >>> ts = TimeSeries(data)
            >>> lm = ts.l_moments(nmom=2)
            >>> lm.index.tolist()
            ['L1', 'L2', 't']
            >>> float(lm.loc["L1", "Series1"])
            5.5

            ```
        - Symmetric data has L-skewness near zero:
            ```python
            >>> import numpy as np
            >>> from statista.time_series import TimeSeries
            >>> data = np.array([-5., -4., -3., -2., -1., 0., 1., 2., 3., 4., 5.])
            >>> ts = TimeSeries(data)
            >>> lm = ts.l_moments(nmom=4)
            >>> round(float(lm.loc["t3", "Series1"]), 4)
            0.0

            ```

    References:
        Hosking, J.R.M. (1990). L-moments: Analysis and estimation of
        distributions using linear combinations of order statistics. Journal
        of the Royal Statistical Society, Series B, 52(1), 105-124.

    See Also:
        extended_stats: Conventional moments (skewness, kurtosis) and percentiles.
        summary: Combined table of extended_stats + L-moment ratios.
    """
    if nmom < 2:
        raise ValueError("nmom must be >= 2")

    row_names = ["L1", "L2"]
    if nmom >= 2:
        row_names.append("t")
    if nmom >= 3:
        row_names.append("t3")
    if nmom >= 4:
        row_names.append("t4")
    if nmom >= 5:
        row_names.append("t5")

    result = DataFrame(index=row_names, columns=self.columns, dtype=float)

    for col in self.columns:
        data = self[col].dropna().values
        lmom_calc = Lmoments(data)
        lmoms = lmom_calc.calculate(nmom=nmom)

        l1 = lmoms[0]
        l2 = lmoms[1]
        result.loc["L1", col] = l1
        result.loc["L2", col] = l2
        result.loc["t", col] = l2 / l1 if not np.isclose(l1, 0.0) else np.nan
        if nmom >= 3:
            result.loc["t3", col] = (
                lmoms[2] / l2 if not np.isclose(l2, 0.0) else np.nan
            )
        if nmom >= 4:
            result.loc["t4", col] = (
                lmoms[3] / l2 if not np.isclose(l2, 0.0) else np.nan
            )
        if nmom >= 5:
            result.loc["t5", col] = (
                lmoms[4] / l2 if not np.isclose(l2, 0.0) else np.nan
            )

    return result
summary() #

Comprehensive summary table suitable for a research paper.

Combines extended_stats and l_moments into a single table with 13 rows per column. This produces the kind of "Table 1" that goes into a paper's methods or study-area section.

Returns:

Type Description
DataFrame

pandas.DataFrame: One column per series. Rows: count, mean, std, cv, skewness, kurtosis, min, max, iqr, mad, L-CV, L-skewness, L-kurtosis.

Examples:

  • Generate a paper-ready summary from real data: 
    >>> import numpy as np
>>> from statista.time_series import TimeSeries
>>> data = np.loadtxt("examples/data/time_series1.txt")
>>> ts = TimeSeries(data)
>>> sm = ts.summary()
>>> sm.index.tolist()
['count', 'mean', 'std', 'cv', 'skewness', 'kurtosis', 'min', 'max', 'iqr', 'mad', 'L-CV', 'L-skewness', 'L-kurtosis']
>>> len(sm)
13
>>> round(float(sm.loc["L-skewness", "Series1"]), 4)
0.4815
  • Multi-column summary for comparing stations: 
    >>> import numpy as np
>>> from statista.time_series import TimeSeries
>>> np.random.seed(42)
>>> data = np.column_stack([np.random.randn(100) * 10 + 50,
...                         np.random.randn(100) * 5 + 20])
>>> ts = TimeSeries(data, columns=["Flow", "Temp"])
>>> sm = ts.summary()
>>> sm.columns.tolist()
['Flow', 'Temp']
>>> round(float(sm.loc["mean", "Flow"]), 2)
48.96
See Also

extended_stats: The 17-row conventional statistics table. l_moments: L-moment ratios independently.

Source code in src\statista\time_series\descriptive.py 
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def summary(self) -> DataFrame:
    """Comprehensive summary table suitable for a research paper.

    Combines ``extended_stats`` and ``l_moments`` into a single table with
    13 rows per column. This produces the kind of "Table 1" that goes into
    a paper's methods or study-area section.

    Returns:
        pandas.DataFrame:
            One column per series. Rows: count, mean, std, cv, skewness,
            kurtosis, min, max, iqr, mad, L-CV, L-skewness, L-kurtosis.

    Examples:
        - Generate a paper-ready summary from real data:
            ```python
            >>> import numpy as np
            >>> from statista.time_series import TimeSeries
            >>> data = np.loadtxt("examples/data/time_series1.txt")
            >>> ts = TimeSeries(data)
            >>> sm = ts.summary()
            >>> sm.index.tolist()
            ['count', 'mean', 'std', 'cv', 'skewness', 'kurtosis', 'min', 'max', 'iqr', 'mad', 'L-CV', 'L-skewness', 'L-kurtosis']
            >>> len(sm)
            13
            >>> round(float(sm.loc["L-skewness", "Series1"]), 4)
            0.4815

            ```
        - Multi-column summary for comparing stations:
            ```python
            >>> import numpy as np
            >>> from statista.time_series import TimeSeries
            >>> np.random.seed(42)
            >>> data = np.column_stack([np.random.randn(100) * 10 + 50,
            ...                         np.random.randn(100) * 5 + 20])
            >>> ts = TimeSeries(data, columns=["Flow", "Temp"])
            >>> sm = ts.summary()
            >>> sm.columns.tolist()
            ['Flow', 'Temp']
            >>> round(float(sm.loc["mean", "Flow"]), 2)
            48.96

            ```

    See Also:
        extended_stats: The 17-row conventional statistics table.
        l_moments: L-moment ratios independently.
    """
    estats = self.extended_stats
    lmom = self.l_moments(nmom=4)

    summary_rows = [
        "count",
        "mean",
        "std",
        "cv",
        "skewness",
        "kurtosis",
        "min",
        "max",
        "iqr",
        "mad",
    ]
    result = estats.loc[summary_rows, :].copy()

    result.loc["L-CV"] = lmom.loc["t"]
    result.loc["L-skewness"] = lmom.loc["t3"]
    result.loc["L-kurtosis"] = lmom.loc["t4"]

    return result