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Confidence Interval#

statista.confidence_interval.ConfidenceInterval #

ConfidenceInterval.

Source code in src/statista/confidence_interval.py 
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class ConfidenceInterval:
    """ConfidenceInterval."""

    @staticmethod
    def bs_indexes(data: np.ndarray, n_samples: int = 10000):
        """bs_indexes.

            - generate random indeces to shuffle the data of the given array.
            - using the indeces, you can access the given data array and get randomly generated data from the
            original given data.
            - Given data points data, where axis 0 is considered to delineate points, return a generator for
            sets of bootstrap indexes.

        This can be used as a list of bootstrap indexes (with
        list(bootstrap_indexes(data))) as well.

        Returns:
            np.ndarray:
                array with the same length as the input data, containing integer indices.

        Examples:
            ```python
            >>> from statista.confidence_interval import ConfidenceInterval
            >>> data = [3.1, 2.4, 5.6, 8.4]
            >>> indices = ConfidenceInterval.bs_indexes(data, n_samples=2)

            ```
        """
        for _ in range(n_samples):
            yield randint(data.shape[0], size=(data.shape[0],))

    @staticmethod
    def boot_strap(
        data: list | np.ndarray,
        state_function: Callable,
        alpha: float = 0.05,
        n_samples: int = 100,
        **kwargs,
    ):  # ->  Dict[str, OrderedDict[str, Tuple[Any, Any]]]
        """boot_strap

        Calculate confidence intervals using parametric bootstrap and the percentile interval method This is used to
        get confidence intervals for the estimators and the return values for several return values.

        More info about bootstrapping can be found on:
            - Efron: "An Introduction to the Bootstrap", Chapman & Hall (1993)
            - https://en.wikipedia.org/wiki/Bootstrapping_%28statistics%29

        Args:
            data (list, np.ndarray):
                data to be used to calculate the confidence interval
            state_function (callable):
                function to be used to calculate the confidence interval
            n_samples (int):
                number of samples to be generated. Default is 100.
            alpha (numeric, optional):
                alpha or SignificanceLevel is a value of the confidence interval. Default is 0.05
            **kwargs:
                gevfit (list):
                    Three parameters of the GEV distribution [shape, loc, scale]
                F (list):
                    non-exceedance probability/ cdf
                method (str):
                    method used to fit the generated samples from the bootstrap method ["lmoments", "mle", "mm"]. Default is
                    "lmoments".
        """
        alphas = np.array([alpha / 2, 1 - alpha / 2])
        tdata = (np.array(data),)

        # We don't need to generate actual samples; that would take more memory.
        # Instead, we can generate just the indexes and then apply the stat-fun
        # to those indexes.
        boot_indexes = ConfidenceInterval.bs_indexes(tdata[0], n_samples)
        stat = np.array(
            [
                state_function(*(x[indexes] for x in tdata), **kwargs)
                for indexes in boot_indexes
            ]
        )
        stat.sort(axis=0)

        # Percentile Interval Method
        a_vals = alphas
        n_vals = np.round((n_samples - 1) * a_vals).astype("int")

        if np.any(n_vals == 0) or np.any(n_vals == n_samples - 1):
            logger.debug(
                "Some values used extreme samples; results are probably unstable."
            )

        elif np.any(n_vals < 10) or np.any(n_vals >= n_samples - 10):
            logger.debug(
                "Some values used the top 10 low/high samples; results may be unstable."
            )

        if n_vals.ndim == 1:
            # All n_vals are the same. Simple broadcasting
            out = stat[n_vals]
        else:
            # n_vals are different for each data point. Not simple broadcasting.
            # Each set of n_vals along axis 0 corresponds to the data at the same
            # point in other axes.
            out = stat[(n_vals, np.indices(n_vals.shape)[1:].squeeze())]

        ub = out[0, 3:]
        lb = out[1, 3:]
        params = OrderedDict()
        params["shape"] = (out[0, 0], out[1, 0])
        params["location"] = (out[0, 1], out[1, 1])
        params["scale"] = (out[0, 2], out[1, 2])

        return {"lb": lb, "ub": ub, "params": params}

bs_indexes(data, n_samples=10000) staticmethod #

bs_indexes.

- generate random indeces to shuffle the data of the given array.
- using the indeces, you can access the given data array and get randomly generated data from the
original given data.
- Given data points data, where axis 0 is considered to delineate points, return a generator for
sets of bootstrap indexes.

This can be used as a list of bootstrap indexes (with list(bootstrap_indexes(data))) as well.

Returns:

Type Description

np.ndarray: array with the same length as the input data, containing integer indices.

Examples:

>>> from statista.confidence_interval import ConfidenceInterval
>>> data = [3.1, 2.4, 5.6, 8.4]
>>> indices = ConfidenceInterval.bs_indexes(data, n_samples=2)
Source code in src/statista/confidence_interval.py 
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@staticmethod
def bs_indexes(data: np.ndarray, n_samples: int = 10000):
    """bs_indexes.

        - generate random indeces to shuffle the data of the given array.
        - using the indeces, you can access the given data array and get randomly generated data from the
        original given data.
        - Given data points data, where axis 0 is considered to delineate points, return a generator for
        sets of bootstrap indexes.

    This can be used as a list of bootstrap indexes (with
    list(bootstrap_indexes(data))) as well.

    Returns:
        np.ndarray:
            array with the same length as the input data, containing integer indices.

    Examples:
        ```python
        >>> from statista.confidence_interval import ConfidenceInterval
        >>> data = [3.1, 2.4, 5.6, 8.4]
        >>> indices = ConfidenceInterval.bs_indexes(data, n_samples=2)

        ```
    """
    for _ in range(n_samples):
        yield randint(data.shape[0], size=(data.shape[0],))

boot_strap(data, state_function, alpha=0.05, n_samples=100, **kwargs) staticmethod #

boot_strap

Calculate confidence intervals using parametric bootstrap and the percentile interval method This is used to get confidence intervals for the estimators and the return values for several return values.

More info about bootstrapping can be found on
  • Efron: "An Introduction to the Bootstrap", Chapman & Hall (1993)
  • https://en.wikipedia.org/wiki/Bootstrapping_%28statistics%29

Parameters:

Name Type Description Default
data (list, ndarray)

data to be used to calculate the confidence interval

 required
state_function callable

function to be used to calculate the confidence interval

 required
n_samples int

number of samples to be generated. Default is 100.

 100
alpha numeric

alpha or SignificanceLevel is a value of the confidence interval. Default is 0.05

 0.05
**kwargs

gevfit (list): Three parameters of the GEV distribution [shape, loc, scale] F (list): non-exceedance probability/ cdf method (str): method used to fit the generated samples from the bootstrap method ["lmoments", "mle", "mm"]. Default is "lmoments".

 {}
Source code in src/statista/confidence_interval.py 
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@staticmethod
def boot_strap(
    data: list | np.ndarray,
    state_function: Callable,
    alpha: float = 0.05,
    n_samples: int = 100,
    **kwargs,
):  # ->  Dict[str, OrderedDict[str, Tuple[Any, Any]]]
    """boot_strap

    Calculate confidence intervals using parametric bootstrap and the percentile interval method This is used to
    get confidence intervals for the estimators and the return values for several return values.

    More info about bootstrapping can be found on:
        - Efron: "An Introduction to the Bootstrap", Chapman & Hall (1993)
        - https://en.wikipedia.org/wiki/Bootstrapping_%28statistics%29

    Args:
        data (list, np.ndarray):
            data to be used to calculate the confidence interval
        state_function (callable):
            function to be used to calculate the confidence interval
        n_samples (int):
            number of samples to be generated. Default is 100.
        alpha (numeric, optional):
            alpha or SignificanceLevel is a value of the confidence interval. Default is 0.05
        **kwargs:
            gevfit (list):
                Three parameters of the GEV distribution [shape, loc, scale]
            F (list):
                non-exceedance probability/ cdf
            method (str):
                method used to fit the generated samples from the bootstrap method ["lmoments", "mle", "mm"]. Default is
                "lmoments".
    """
    alphas = np.array([alpha / 2, 1 - alpha / 2])
    tdata = (np.array(data),)

    # We don't need to generate actual samples; that would take more memory.
    # Instead, we can generate just the indexes and then apply the stat-fun
    # to those indexes.
    boot_indexes = ConfidenceInterval.bs_indexes(tdata[0], n_samples)
    stat = np.array(
        [
            state_function(*(x[indexes] for x in tdata), **kwargs)
            for indexes in boot_indexes
        ]
    )
    stat.sort(axis=0)

    # Percentile Interval Method
    a_vals = alphas
    n_vals = np.round((n_samples - 1) * a_vals).astype("int")

    if np.any(n_vals == 0) or np.any(n_vals == n_samples - 1):
        logger.debug(
            "Some values used extreme samples; results are probably unstable."
        )

    elif np.any(n_vals < 10) or np.any(n_vals >= n_samples - 10):
        logger.debug(
            "Some values used the top 10 low/high samples; results may be unstable."
        )

    if n_vals.ndim == 1:
        # All n_vals are the same. Simple broadcasting
        out = stat[n_vals]
    else:
        # n_vals are different for each data point. Not simple broadcasting.
        # Each set of n_vals along axis 0 corresponds to the data at the same
        # point in other axes.
        out = stat[(n_vals, np.indices(n_vals.shape)[1:].squeeze())]

    ub = out[0, 3:]
    lb = out[1, 3:]
    params = OrderedDict()
    params["shape"] = (out[0, 0], out[1, 0])
    params["location"] = (out[0, 1], out[1, 1])
    params["scale"] = (out[0, 2], out[1, 2])

    return {"lb": lb, "ub": ub, "params": params}