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�Z&�xZ'S)y�	Expandinga�
    Provide expanding window calculations.

    Parameters
    ----------
    min_periods : int, default 1
        Minimum number of observations in window required to have a value;
        otherwise, result is ``np.nan``.

    axis : int or str, default 0
        If ``0`` or ``'index'``, roll across the rows.

        If ``1`` or ``'columns'``, roll across the columns.

        For `Series` this parameter is unused and defaults to 0.

    method : str {'single', 'table'}, default 'single'
        Execute the rolling operation per single column or row (``'single'``)
        or over the entire object (``'table'``).

        This argument is only implemented when specifying ``engine='numba'``
        in the method call.

        .. versionadded:: 1.3.0

    Returns
    -------
    pandas.api.typing.Expanding

    See Also
    --------
    rolling : Provides rolling window calculations.
    ewm : Provides exponential weighted functions.

    Notes
    -----
    See :ref:`Windowing Operations <window.expanding>` for further usage details
    and examples.

    Examples
    --------
    >>> df = pd.DataFrame({"B": [0, 1, 2, np.nan, 4]})
    >>> df
         B
    0  0.0
    1  1.0
    2  2.0
    3  NaN
    4  4.0

    **min_periods**

    Expanding sum with 1 vs 3 observations needed to calculate a value.

    >>> df.expanding(1).sum()
         B
    0  0.0
    1  1.0
    2  3.0
    3  3.0
    4  7.0
    >>> df.expanding(3).sum()
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    4  7.0
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        >>> df
           A  B  C
        0  1  4  7
        1  2  5  8
        2  3  6  9

        >>> df.ewm(alpha=0.5).mean()
                  A         B         C
        0  1.000000  4.000000  7.000000
        1  1.666667  4.666667  7.666667
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        b    0.0
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        d    2.0
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        The default ``ddof`` of 1 used in :meth:`Series.std` is different
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        >>> s = pd.Series([5, 5, 6, 7, 5, 5, 5])

        >>> s.expanding(3).std()
        0         NaN
        1         NaN
        2    0.577350
        3    0.957427
        4    0.894427
        5    0.836660
        6    0.786796
        dtype: float64
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        The default ``ddof`` of 1 used in :meth:`Series.var` is different
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        >>> s = pd.Series([5, 5, 6, 7, 5, 5, 5])

        >>> s.expanding(3).var()
        0         NaN
        1         NaN
        2    0.333333
        3    0.916667
        4    0.800000
        5    0.700000
        6    0.619048
        dtype: float64
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Expanding.var�rar.z:A minimum of one period is required for the calculation.

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        >>> s = pd.Series([0, 1, 2, 3])

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        0         NaN
        1    0.707107
        2    0.707107
        3    0.745356
        dtype: float64
        zstandard error of mean�semc�&��t�|�||��S)N)r_rC)r)re)r+r_rCr,s   �r-rez
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a        >>> ser = pd.Series([-1, 0, 2, -1, 2], index=['a', 'b', 'c', 'd', 'e'])
        >>> ser.expanding().skew()
        a         NaN
        b         NaN
        c    0.935220
        d    1.414214
        e    0.315356
        dtype: float64
        zunbiased skewness�skewc�$��t�|�|��SrB)r)rgrDs  �r-rgzExpanding.skewYs���:�w�|��|�6�6r.z/scipy.stats.kurtosis : Reference SciPy method.
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        The example below will show a rolling calculation with a window size of
        four matching the equivalent function call using `scipy.stats`.

        >>> arr = [1, 2, 3, 4, 999]
        >>> import scipy.stats
        >>> print(f"{{scipy.stats.kurtosis(arr[:-1], bias=False):.6f}}")
        -1.200000
        >>> print(f"{{scipy.stats.kurtosis(arr, bias=False):.6f}}")
        4.999874
        >>> s = pd.Series(arr)
        >>> s.expanding(4).kurt()
        0         NaN
        1         NaN
        2         NaN
        3   -1.200000
        4    4.999874
        dtype: float64
        z,Fisher's definition of kurtosis without bias�kurtc�$��t�|�|��SrB)r)rirDs  �r-rizExpanding.kurtxs���L�w�|��|�6�6r.a�
        quantile : float
            Quantile to compute. 0 <= quantile <= 1.

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                This will be renamed to 'q' in a future version.
        interpolation : {{'linear', 'lower', 'higher', 'midpoint', 'nearest'}}
            This optional parameter specifies the interpolation method to use,
            when the desired quantile lies between two data points `i` and `j`:

                * linear: `i + (j - i) * fraction`, where `fraction` is the
                  fractional part of the index surrounded by `i` and `j`.
                * lower: `i`.
                * higher: `j`.
                * nearest: `i` or `j` whichever is nearest.
                * midpoint: (`i` + `j`) / 2.
        a        >>> ser = pd.Series([1, 2, 3, 4, 5, 6], index=['a', 'b', 'c', 'd', 'e', 'f'])
        >>> ser.expanding(min_periods=4).quantile(.25)
        a     NaN
        b     NaN
        c     NaN
        d    1.75
        e    2.00
        f    2.25
        dtype: float64
        �quantile�q)�old_arg_name�new_arg_namec�(��t�|�|||��S)N)rl�
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        method : {{'average', 'min', 'max'}}, default 'average'
            How to rank the group of records that have the same value (i.e. ties):

            * average: average rank of the group
            * min: lowest rank in the group
            * max: highest rank in the group

        ascending : bool, default True
            Whether or not the elements should be ranked in ascending order.
        pct : bool, default False
            Whether or not to display the returned rankings in percentile
            form.
        a+
        >>> s = pd.Series([1, 4, 2, 3, 5, 3])
        >>> s.expanding().rank()
        0    1.0
        1    2.0
        2    2.0
        3    3.0
        4    5.0
        5    3.5
        dtype: float64

        >>> s.expanding().rank(method="max")
        0    1.0
        1    2.0
        2    2.0
        3    3.0
        4    5.0
        5    4.0
        dtype: float64

        >>> s.expanding().rank(method="min")
        0    1.0
        1    2.0
        2    2.0
        3    3.0
        4    5.0
        5    3.0
        dtype: float64
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        other : Series or DataFrame, optional
            If not supplied then will default to self and produce pairwise
            output.
        pairwise : bool, default None
            If False then only matching columns between self and other will be
            used and the output will be a DataFrame.
            If True then all pairwise combinations will be calculated and the
            output will be a MultiIndexed DataFrame in the case of DataFrame
            inputs. In the case of missing elements, only complete pairwise
            observations will be used.
        ddof : int, default 1
            Delta Degrees of Freedom.  The divisor used in calculations
            is ``N - ddof``, where ``N`` represents the number of elements.
        a0        >>> ser1 = pd.Series([1, 2, 3, 4], index=['a', 'b', 'c', 'd'])
        >>> ser2 = pd.Series([10, 11, 13, 16], index=['a', 'b', 'c', 'd'])
        >>> ser1.expanding().cov(ser2)
        a         NaN
        b    0.500000
        c    1.500000
        d    3.333333
        dtype: float64
        zsample covariance�covc�*��t�|�||||��S�N)�other�pairwiser_rC)r)ru�r+rxryr_rCr,s     �r-ruz
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        other : Series or DataFrame, optional
            If not supplied then will default to self and produce pairwise
            output.
        pairwise : bool, default None
            If False then only matching columns between self and other will be
            used and the output will be a DataFrame.
            If True then all pairwise combinations will be calculated and the
            output will be a MultiIndexed DataFrame in the case of DataFrame
            inputs. In the case of missing elements, only complete pairwise
            observations will be used.
        z�
        cov : Similar method to calculate covariance.
        numpy.corrcoef : NumPy Pearson's correlation calculation.
        ao
        This function uses Pearson's definition of correlation
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        When `other` is not specified, the output will be self correlation (e.g.
        all 1's), except for :class:`~pandas.DataFrame` inputs with `pairwise`
        set to `True`.

        Function will return ``NaN`` for correlations of equal valued sequences;
        this is the result of a 0/0 division error.

        When `pairwise` is set to `False`, only matching columns between `self` and
        `other` will be used.

        When `pairwise` is set to `True`, the output will be a MultiIndex DataFrame
        with the original index on the first level, and the `other` DataFrame
        columns on the second level.

        In the case of missing elements, only complete pairwise observations
        will be used.

        a1        >>> ser1 = pd.Series([1, 2, 3, 4], index=['a', 'b', 'c', 'd'])
        >>> ser2 = pd.Series([10, 11, 13, 16], index=['a', 'b', 'c', 'd'])
        >>> ser1.expanding().corr(ser2)
        a         NaN
        b    1.000000
        c    0.981981
        d    0.975900
        dtype: float64
        �correlation�corrc�*��t�|�||||��Srw)r)r|rzs     �r-r|zExpanding.corr]s(���X�w�|����%�	�
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