def _log_prob_with_logsf_and_logcdf(self, y):
    """"""
    # There are two options that would be equal if we had infinite precision:
    # Log[ sf(y - 1) - sf(y) ]
    #   = Log[ exp{logsf(y - 1)} - exp{logsf(y)} ]
    # Log[ cdf(y) - cdf(y - 1) ]
    #   = Log[ exp{logcdf(y)} - exp{logcdf(y - 1)} ]
    logsf_y = self.log_survival_function(y)
    logsf_y_minus_1 = self.log_survival_function(y - 1)
    logcdf_y = self.log_cdf(y)
    logcdf_y_minus_1 = self.log_cdf(y - 1)

    # Important:  Here we use select in a way such that no input is inf, this
    # prevents the troublesome case where the output of select can be finite,
    # but the output of grad(select) will be NaN.

    # In either case, we are doing Log[ exp{big} - exp{small} ]
    # We want to use the sf items precisely when we are on the right side of the
    # median, which occurs when logsf_y < logcdf_y.
    big = tf.where(logsf_y < logcdf_y, logsf_y_minus_1, logcdf_y)
    small = tf.where(logsf_y < logcdf_y, logsf_y, logcdf_y_minus_1)

    return _logsum_expbig_minus_expsmall(big, small)