LAUSR

Abstract A continuous random variable can be uniquely represented by the score function of distribution, i.e. a scalar-valued function describing the influence of a data item on the typical value of the distribution. There are at most two relevant scalar-valued scores based on two basic transformations: the “natural” one, useful for estimating parameters of parametric distributions by the generalized moment method; and the “universal” one, which is a basis for the score function of distribution. The score mean, the zero of the score function of distribution, represents the typical value of the distribution in the sense of the value which is most likely to be sampled. Both scores are often identical to each other. The derivative of the score function of distribution is the weight function of this distribution. The main result is that sums of score random variables obey the central limit theorem and can be used for directly estimating the score mean without use of any current estimator.