Evaluation of the quality of small samples of biometric data using a differential variant statistical test of the geometric mean

One of the most popular in the statistical analysis of the data is the Pearson criterion. Chi-square Pearson entirely devoted to the first part of the State Standard of the recommendation, while all other criteria are described in the second part of the recommendations. The purpose is to assess the capacity of the two variants of the statistical criteria of the geometric mean of the empirical and theoretical probability functions. We investigate the power of the Cramer criteria - Mizesa background, created in 1928, and the geometric mean criterion proposed in 2014. A comparison is carried out for small test samples, typical of the biometric data. It is proposed to use simulation tools and numerically to estimate power at comparable criteria equally errors of the first and second kind. Applying a logarithmic scale comparative assessment of capacities, which, depending on the number of power compared experiences in the training set are close to linear. It is shown that the statistical test of the geometric mean of the compared probability functions previously proposed inferior to power its analogue differential. The greatest power of suppressing quantization noise has a criterion, built as a geometric mean of comparable probability density function. The considered criteria in their multidimensional embodiment are capable of operating at extremely small samples of biometric data from 11 to 21, an example of a biometric image.