Optimal Histogram Filter

Abstract

The article discusses a technique for constructing an optimal histogram filter and its modifications, taking into account a priori information about the expected probability distribution density. The main idea of constructing a histogram filter is to apply a special transformation that displays the profile of a section of any distribution law into a constant level of characteristic numbers equivalent to it. This transformation allows to determine the coefficients of the histogram filter. An estimate of the value of the number of data of a particular interval of the histogram is formed by the characteristic function of the filter containing real data and equivalent to the characteristic number. The convergence of the estimates obtained by the histogram filter to the true values of the interval probabilities is shown. Modifications of the optimal histogram filter that require less computational costs for their implementation are considered. The upper bounds of the qualitative characteristics of filters are obtained. It has been established that the optimal histogram filter, regardless of the type of distribution law, provides three times the best quality of identification (recognition) in comparison with the standard histogram estimate. The efficiency of the histogram filter is confirmed by simulations. The histogram filter is an easy-to-implement tool that can be easily integrated into any open distribution law identification (recognition) algorithm.