Generate descriptive statistics that summarize the central tendency,
        dispersion and shape of a dataset's distribution, excluding
        ``NaN`` values.

        Analyzes both numeric and object series, as well
        as ``DataFrame`` column sets of mixed data types. The output
        will vary depending on what is provided. Refer to the notes
        below for more detail.

        Parameters
        ----------
        percentiles : list-like of numbers, optional
            The percentiles to include in the output. All should
            fall between 0 and 1. The default is
            ``[.25, .5, .75]``, which returns the 25th, 50th, and
            75th percentiles.
        include : 'all', list-like of dtypes or None (default), optional
            A white list of data types to include in the result. Ignored
            for ``Series``. Here are the options:

            - 'all' : All columns of the input will be included in the output.
            - A list-like of dtypes : Limits the results to the
              provided data types.
              To limit the result to numeric types submit
              ``numpy.number``. To limit it instead to object columns submit
              the ``numpy.object`` data type. Strings
              can also be used in the style of
              ``select_dtypes`` (e.g. ``df.describe(include=['O'])``). To
              select pandas categorical columns, use ``'category'``
            - None (default) : The result will include all numeric columns.
        exclude : list-like of dtypes or None (default), optional,
            A black list of data types to omit from the result. Ignored
            for ``Series``. Here are the options:

            - A list-like of dtypes : Excludes the provided data types
              from the result. To exclude numeric types submit
              ``numpy.number``. To exclude object columns submit the data
              type ``numpy.object``. Strings can also be used in the style of
              ``select_dtypes`` (e.g. ``df.describe(include=['O'])``). To
              exclude pandas categorical columns, use ``'category'``
            - None (default) : The result will exclude nothing.

        Returns
        -------
        Series or DataFrame
            Summary statistics of the Series or Dataframe provided.

        See Also
        --------
        DataFrame.count: Count number of non-NA/null observations.
        DataFrame.max: Maximum of the values in the object.
        DataFrame.min: Minimum of the values in the object.
        DataFrame.mean: Mean of the values.
        DataFrame.std: Standard deviation of the obersvations.
        DataFrame.select_dtypes: Subset of a DataFrame including/excluding
            columns based on their dtype.

        Notes
        -----
        For numeric data, the result's index will include ``count``,
        ``mean``, ``std``, ``min``, ``max`` as well as lower, ``50`` and
        upper percentiles. By default the lower percentile is ``25`` and the
        upper percentile is ``75``. The ``50`` percentile is the
        same as the median.

        For object data (e.g. strings or timestamps), the result's index
        will include ``count``, ``unique``, ``top``, and ``freq``. The ``top``
        is the most common value. The ``freq`` is the most common value's
        frequency. Timestamps also include the ``first`` and ``last`` items.

        If multiple object values have the highest count, then the
        ``count`` and ``top`` results will be arbitrarily chosen from
        among those with the highest count.

        For mixed data types provided via a ``DataFrame``, the default is to
        return only an analysis of numeric columns. If the dataframe consists
        only of object and categorical data without any numeric columns, the
        default is to return an analysis of both the object and categorical
        columns. If ``include='all'`` is provided as an option, the result
        will include a union of attributes of each type.

        The `include` and `exclude` parameters can be used to limit
        which columns in a ``DataFrame`` are analyzed for the output.
        The parameters are ignored when analyzing a ``Series``.

        Examples
        --------
        Describing a numeric ``Series``.

        >>> s = pd.Series([1, 2, 3])
        >>> s.describe()
        count    3.0
        mean     2.0
        std      1.0
        min      1.0
        25%      1.5
        50%      2.0
        75%      2.5
        max      3.0
        dtype: float64

        Describing a categorical ``Series``.

        >>> s = pd.Series(['a', 'a', 'b', 'c'])
        >>> s.describe()
        count     4
        unique    3
        top       a
        freq      2
        dtype: object

        Describing a timestamp ``Series``.

        >>> s = pd.Series([
        ...   np.datetime64("2000-01-01"),
        ...   np.datetime64("2010-01-01"),
        ...   np.datetime64("2010-01-01")
        ... ])
        >>> s.describe()
        count                       3
        unique                      2
        top       2010-01-01 00:00:00
        freq                        2
        first     2000-01-01 00:00:00
        last      2010-01-01 00:00:00
        dtype: object

        Describing a ``DataFrame``. By default only numeric fields
        are returned.

        >>> df = pd.DataFrame({'categorical': pd.Categorical(['d','e','f']),
        ...                    'numeric': [1, 2, 3],
        ...                    'object': ['a', 'b', 'c']
        ...                   })
        >>> df.describe()
               numeric
        count      3.0
        mean       2.0
        std        1.0
        min        1.0
        25%        1.5
        50%        2.0
        75%        2.5
        max        3.0

        Describing all columns of a ``DataFrame`` regardless of data type.

        >>> df.describe(include='all')
                categorical  numeric object
        count            3      3.0      3
        unique           3      NaN      3
        top              f      NaN      c
        freq             1      NaN      1
        mean           NaN      2.0    NaN
        std            NaN      1.0    NaN
        min            NaN      1.0    NaN
        25%            NaN      1.5    NaN
        50%            NaN      2.0    NaN
        75%            NaN      2.5    NaN
        max            NaN      3.0    NaN

        Describing a column from a ``DataFrame`` by accessing it as
        an attribute.

        >>> df.numeric.describe()
        count    3.0
        mean     2.0
        std      1.0
        min      1.0
        25%      1.5
        50%      2.0
        75%      2.5
        max      3.0
        Name: numeric, dtype: float64

        Including only numeric columns in a ``DataFrame`` description.

        >>> df.describe(include=[np.number])
               numeric
        count      3.0
        mean       2.0
        std        1.0
        min        1.0
        25%        1.5
        50%        2.0
        75%        2.5
        max        3.0

        Including only string columns in a ``DataFrame`` description.

        >>> df.describe(include=[np.object])
               object
        count       3
        unique      3
        top         c
        freq        1

        Including only categorical columns from a ``DataFrame`` description.

        >>> df.describe(include=['category'])
               categorical
        count            3
        unique           3
        top              f
        freq             1

        Excluding numeric columns from a ``DataFrame`` description.

        >>> df.describe(exclude=[np.number])
               categorical object
        count            3      3
        unique           3      3
        top              f      c
        freq             1      1

        Excluding object columns from a ``DataFrame`` description.

        >>> df.describe(exclude=[np.object])
               categorical  numeric
        count            3      3.0
        unique           3      NaN
        top              f      NaN
        freq             1      NaN
        mean           NaN      2.0
        std            NaN      1.0
        min            NaN      1.0
        25%            NaN      1.5
        50%            NaN      2.0
        75%            NaN      2.5
        max            NaN      3.0

def describe(self, percentiles=None, include=None, exclude=None):
        """
        Generate descriptive statistics that summarize the central tendency,
        dispersion and shape of a dataset's distribution, excluding
        ``NaN`` values.

        Analyzes both numeric and object series, as well
        as ``DataFrame`` column sets of mixed data types. The output
        will vary depending on what is provided. Refer to the notes
        below for more detail.

        Parameters
        ----------
        percentiles : list-like of numbers, optional
            The percentiles to include in the output. All should
            fall between 0 and 1. The default is
            ``[.25, .5, .75]``, which returns the 25th, 50th, and
            75th percentiles.
        include : 'all', list-like of dtypes or None (default), optional
            A white list of data types to include in the result. Ignored
            for ``Series``. Here are the options:

            - 'all' : All columns of the input will be included in the output.
            - A list-like of dtypes : Limits the results to the
              provided data types.
              To limit the result to numeric types submit
              ``numpy.number``. To limit it instead to object columns submit
              the ``numpy.object`` data type. Strings
              can also be used in the style of
              ``select_dtypes`` (e.g. ``df.describe(include=['O'])``). To
              select pandas categorical columns, use ``'category'``
            - None (default) : The result will include all numeric columns.
        exclude : list-like of dtypes or None (default), optional,
            A black list of data types to omit from the result. Ignored
            for ``Series``. Here are the options:

            - A list-like of dtypes : Excludes the provided data types
              from the result. To exclude numeric types submit
              ``numpy.number``. To exclude object columns submit the data
              type ``numpy.object``. Strings can also be used in the style of
              ``select_dtypes`` (e.g. ``df.describe(include=['O'])``). To
              exclude pandas categorical columns, use ``'category'``
            - None (default) : The result will exclude nothing.

        Returns
        -------
        Series or DataFrame
            Summary statistics of the Series or Dataframe provided.

        See Also
        --------
        DataFrame.count: Count number of non-NA/null observations.
        DataFrame.max: Maximum of the values in the object.
        DataFrame.min: Minimum of the values in the object.
        DataFrame.mean: Mean of the values.
        DataFrame.std: Standard deviation of the obersvations.
        DataFrame.select_dtypes: Subset of a DataFrame including/excluding
            columns based on their dtype.

        Notes
        -----
        For numeric data, the result's index will include ``count``,
        ``mean``, ``std``, ``min``, ``max`` as well as lower, ``50`` and
        upper percentiles. By default the lower percentile is ``25`` and the
        upper percentile is ``75``. The ``50`` percentile is the
        same as the median.

        For object data (e.g. strings or timestamps), the result's index
        will include ``count``, ``unique``, ``top``, and ``freq``. The ``top``
        is the most common value. The ``freq`` is the most common value's
        frequency. Timestamps also include the ``first`` and ``last`` items.

        If multiple object values have the highest count, then the
        ``count`` and ``top`` results will be arbitrarily chosen from
        among those with the highest count.

        For mixed data types provided via a ``DataFrame``, the default is to
        return only an analysis of numeric columns. If the dataframe consists
        only of object and categorical data without any numeric columns, the
        default is to return an analysis of both the object and categorical
        columns. If ``include='all'`` is provided as an option, the result
        will include a union of attributes of each type.

        The `include` and `exclude` parameters can be used to limit
        which columns in a ``DataFrame`` are analyzed for the output.
        The parameters are ignored when analyzing a ``Series``.

        Examples
        --------
        Describing a numeric ``Series``.

        >>> s = pd.Series([1, 2, 3])
        >>> s.describe()
        count    3.0
        mean     2.0
        std      1.0
        min      1.0
        25%      1.5
        50%      2.0
        75%      2.5
        max      3.0
        dtype: float64

        Describing a categorical ``Series``.

        >>> s = pd.Series(['a', 'a', 'b', 'c'])
        >>> s.describe()
        count     4
        unique    3
        top       a
        freq      2
        dtype: object

        Describing a timestamp ``Series``.

        >>> s = pd.Series([
        ...   np.datetime64("2000-01-01"),
        ...   np.datetime64("2010-01-01"),
        ...   np.datetime64("2010-01-01")
        ... ])
        >>> s.describe()
        count                       3
        unique                      2
        top       2010-01-01 00:00:00
        freq                        2
        first     2000-01-01 00:00:00
        last      2010-01-01 00:00:00
        dtype: object

        Describing a ``DataFrame``. By default only numeric fields
        are returned.

        >>> df = pd.DataFrame({'categorical': pd.Categorical(['d','e','f']),
        ...                    'numeric': [1, 2, 3],
        ...                    'object': ['a', 'b', 'c']
        ...                   })
        >>> df.describe()
               numeric
        count      3.0
        mean       2.0
        std        1.0
        min        1.0
        25%        1.5
        50%        2.0
        75%        2.5
        max        3.0

        Describing all columns of a ``DataFrame`` regardless of data type.

        >>> df.describe(include='all')
                categorical  numeric object
        count            3      3.0      3
        unique           3      NaN      3
        top              f      NaN      c
        freq             1      NaN      1
        mean           NaN      2.0    NaN
        std            NaN      1.0    NaN
        min            NaN      1.0    NaN
        25%            NaN      1.5    NaN
        50%            NaN      2.0    NaN
        75%            NaN      2.5    NaN
        max            NaN      3.0    NaN

        Describing a column from a ``DataFrame`` by accessing it as
        an attribute.

        >>> df.numeric.describe()
        count    3.0
        mean     2.0
        std      1.0
        min      1.0
        25%      1.5
        50%      2.0
        75%      2.5
        max      3.0
        Name: numeric, dtype: float64

        Including only numeric columns in a ``DataFrame`` description.

        >>> df.describe(include=[np.number])
               numeric
        count      3.0
        mean       2.0
        std        1.0
        min        1.0
        25%        1.5
        50%        2.0
        75%        2.5
        max        3.0

        Including only string columns in a ``DataFrame`` description.

        >>> df.describe(include=[np.object])
               object
        count       3
        unique      3
        top         c
        freq        1

        Including only categorical columns from a ``DataFrame`` description.

        >>> df.describe(include=['category'])
               categorical
        count            3
        unique           3
        top              f
        freq             1

        Excluding numeric columns from a ``DataFrame`` description.

        >>> df.describe(exclude=[np.number])
               categorical object
        count            3      3
        unique           3      3
        top              f      c
        freq             1      1

        Excluding object columns from a ``DataFrame`` description.

        >>> df.describe(exclude=[np.object])
               categorical  numeric
        count            3      3.0
        unique           3      NaN
        top              f      NaN
        freq             1      NaN
        mean           NaN      2.0
        std            NaN      1.0
        min            NaN      1.0
        25%            NaN      1.5
        50%            NaN      2.0
        75%            NaN      2.5
        max            NaN      3.0
        """
        if self.ndim >= 3:
            msg = "describe is not implemented on Panel objects."
            raise NotImplementedError(msg)
        elif self.ndim == 2 and self.columns.size == 0:
            raise ValueError("Cannot describe a DataFrame without columns")

        if percentiles is not None:
            # explicit conversion of `percentiles` to list
            percentiles = list(percentiles)

            # get them all to be in [0, 1]
            self._check_percentile(percentiles)

            # median should always be included
            if 0.5 not in percentiles:
                percentiles.append(0.5)
            percentiles = np.asarray(percentiles)
        else:
            percentiles = np.array([0.25, 0.5, 0.75])

        # sort and check for duplicates
        unique_pcts = np.unique(percentiles)
        if len(unique_pcts) < len(percentiles):
            raise ValueError("percentiles cannot contain duplicates")
        percentiles = unique_pcts

        formatted_percentiles = format_percentiles(percentiles)

        def describe_numeric_1d(series):
            stat_index = (['count', 'mean', 'std', 'min'] +
                          formatted_percentiles + ['max'])
            d = ([series.count(), series.mean(), series.std(), series.min()] +
                 series.quantile(percentiles).tolist() + [series.max()])
            return pd.Series(d, index=stat_index, name=series.name)

        def describe_categorical_1d(data):
            names = ['count', 'unique']
            objcounts = data.value_counts()
            count_unique = len(objcounts[objcounts != 0])
            result = [data.count(), count_unique]
            if result[1] > 0:
                top, freq = objcounts.index[0], objcounts.iloc[0]

                if is_datetime64_any_dtype(data):
                    tz = data.dt.tz
                    asint = data.dropna().values.view('i8')
                    top = Timestamp(top)
                    if top.tzinfo is not None and tz is not None:
                        # Don't tz_localize(None) if key is already tz-aware
                        top = top.tz_convert(tz)
                    else:
                        top = top.tz_localize(tz)
                    names += ['top', 'freq', 'first', 'last']
                    result += [top, freq,
                               Timestamp(asint.min(), tz=tz),
                               Timestamp(asint.max(), tz=tz)]
                else:
                    names += ['top', 'freq']
                    result += [top, freq]

            return pd.Series(result, index=names, name=data.name)

        def describe_1d(data):
            if is_bool_dtype(data):
                return describe_categorical_1d(data)
            elif is_numeric_dtype(data):
                return describe_numeric_1d(data)
            elif is_timedelta64_dtype(data):
                return describe_numeric_1d(data)
            else:
                return describe_categorical_1d(data)

        if self.ndim == 1:
            return describe_1d(self)
        elif (include is None) and (exclude is None):
            # when some numerics are found, keep only numerics
            data = self.select_dtypes(include=[np.number])
            if len(data.columns) == 0:
                data = self
        elif include == 'all':
            if exclude is not None:
                msg = "exclude must be None when include is 'all'"
                raise ValueError(msg)
            data = self
        else:
            data = self.select_dtypes(include=include, exclude=exclude)

        ldesc = [describe_1d(s) for _, s in data.iteritems()]
        # set a convenient order for rows
        names = []
        ldesc_indexes = sorted((x.index for x in ldesc), key=len)
        for idxnames in ldesc_indexes:
            for name in idxnames:
                if name not in names:
                    names.append(name)

        d = pd.concat(ldesc, join_axes=pd.Index([names]), axis=1)
        d.columns = data.columns.copy()
        return d