def calc_acceleration_bca(jackknife_replicates):
    """
    Calculate the acceleration constant for the Bias Corrected and Accelerated
    (BCa) bootstrap confidence intervals.

    Parameters
    ----------
    jackknife_replicates : 2D ndarray.
        Each row should correspond to a different jackknife parameter sample,
        formed by deleting a particular observation and then re-estimating the
        desired model. Each column should correspond to an element of the
        parameter vector being estimated.

    Returns
    -------
    acceleration : 1D ndarray.
        There will be one element for each element in `mle_estimate`. Elements
        denote the acceleration factors for each component of the parameter
        vector.

    References
    ----------
    Efron, Bradley, and Robert J. Tibshirani. An Introduction to the Bootstrap.
        CRC press, 1994. Section 14.3, Equation 14.15.
    """
    # Get the mean of the bootstrapped statistics.
    jackknife_mean = jackknife_replicates.mean(axis=0)[None, :]
    # Calculate the differences between the mean of the bootstrapped statistics
    differences = jackknife_mean - jackknife_replicates
    numerator = (differences**3).sum(axis=0)
    denominator = 6 * ((differences**2).sum(axis=0))**1.5
    # guard against division by zero. Note that this guard shouldn't distort
    # the computational results since the numerator should be zero whenever the
    # denominator is zero.
    zero_denom = np.where(denominator == 0)
    denominator[zero_denom] = MIN_COMP_VALUE
    # Compute the acceleration.
    acceleration = numerator / denominator
    return acceleration
Calculate the acceleration constant for the Bias Corrected and Accelerated
    (BCa) bootstrap confidence intervals.

    Parameters
    ----------
    jackknife_replicates : 2D ndarray.
        Each row should correspond to a different jackknife parameter sample,
        formed by deleting a particular observation and then re-estimating the
        desired model. Each column should correspond to an element of the
        parameter vector being estimated.

    Returns
    -------
    acceleration : 1D ndarray.
        There will be one element for each element in `mle_estimate`. Elements
        denote the acceleration factors for each component of the parameter
        vector.

    References
    ----------
    Efron, Bradley, and Robert J. Tibshirani. An Introduction to the Bootstrap.
        CRC press, 1994. Section 14.3, Equation 14.15.