Histogram Filter with Smoothing Parameter Setting

A histogram filter with smoothing parameter settings is discussed in the article. The histogram filter can be effectively applied in the problems of identification (recognition) of distribution laws for small amounts of data. The smoothing parameter is determined taking into account the available a priori information regarding the proposed distribution law. The relationship between the mathematical expectations of the chi-square fit criterion of the standard estimation histogram and the use of the histogram filter has been determined. This ratio is determined by the smoothing factor. The numerical value of the smoothing coefficient depends on the following parameters: the amount of data, the number of grouping intervals, and the shape parameters of the distribution law. The paper analyzes the feasibility of using a histogram filter, depending on the ratio of the above parameters. The dependence of the smoothing coefficient on the specified parameters allows one to determine the relationship between the number of data grouping intervals and their volume. The histogram filter is an easy-to-implement tool that can be easily integrated into any open distribution law identification (recognition) algorithm