High Quality Content by WIKIPEDIA articles! In statistics, additive smoothing, sometimes called Lidstone smoothing after George James Lidstone, is a technique used to smooth categorical data. Given an observation x = (x1, …, xd) from a multinomial distribution with N trials and parameter vector ? = (?1, …, ?d), a "smoothed" version of the data gives the estimator: where ? > 0 is the smoothing parameter (? = 0 corresponds to no smoothing). Additive smoothing is a type of shrinkage estimator, as the resulting estimate will be between the empirical estimate xi/n, and the uniform probability 1/d. Using Laplace's rule of succession, some authors have argued that ? should be 1, though in practice a smaller value is typically chosen. From a Bayesian point of view, this corresponds to the expected value of the posterior distribution, using a Dirichlet distribution with parameter ? as a prior.

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