We suggest using two other versions of the Anderson-Darling statistic (which we
refer to as the “upper tail” Anderson-Darling statistic) in which the weighting function is proportional to
the weight of only the upper tail of the distribution. A supremum and quadratic versions of the statistic
are proposed. Such statistic is convenient to use when it is necessary to examine the goodness of fit of a
distribution in the right tail of the data, while the fit in the left tail is unimportant.