def center_mass_exp(interval, scale=1.0):
    """ Calculate the center of mass of negative exponential distribution
        p(x) = exp(-x / scale) / scale
        in the interval of (interval_left, interval_right).
        scale is the same scale parameter as scipy.stats.expon.pdf

    Parameters
    ----------

    interval: size 2 tuple, float
        interval must be in the form of (interval_left, interval_right),
        where interval_left/interval_right is the starting/end point of the
        interval in which the center of mass is calculated for exponential
        distribution.
        Note that interval_left must be non-negative, since exponential is
        not supported in the negative domain, and interval_right must be
        bigger than interval_left (thus positive) to form a well-defined
        interval.
    scale: float, positive
        The scale parameter of the exponential distribution. See above.

    Returns
    -------

    m: float
        The center of mass in the interval of (interval_left,
        interval_right) for exponential distribution.
    """
    assert isinstance(interval, tuple), 'interval must be a tuple'
    assert len(interval) == 2, 'interval must be length two'
    (interval_left, interval_right) = interval
    assert interval_left >= 0, 'interval_left must be non-negative'
    assert interval_right > interval_left, \
        'interval_right must be bigger than interval_left'
    assert scale > 0, 'scale must be positive'

    if interval_right < np.inf:
        return ((interval_left + scale) * np.exp(-interval_left / scale) - (
            scale + interval_right) * np.exp(-interval_right / scale)) / (
            np.exp(-interval_left / scale) - np.exp(-interval_right / scale))
    else:
        return interval_left + scale
Calculate the center of mass of negative exponential distribution
        p(x) = exp(-x / scale) / scale
        in the interval of (interval_left, interval_right).
        scale is the same scale parameter as scipy.stats.expon.pdf

    Parameters
    ----------

    interval: size 2 tuple, float
        interval must be in the form of (interval_left, interval_right),
        where interval_left/interval_right is the starting/end point of the
        interval in which the center of mass is calculated for exponential
        distribution.
        Note that interval_left must be non-negative, since exponential is
        not supported in the negative domain, and interval_right must be
        bigger than interval_left (thus positive) to form a well-defined
        interval.
    scale: float, positive
        The scale parameter of the exponential distribution. See above.

    Returns
    -------

    m: float
        The center of mass in the interval of (interval_left,
        interval_right) for exponential distribution.