Testing for Hardy-Weinberg equilibrium.

The class of admissible tests for Hardy-Weinberg equilibrium in a multi-allelic system is characterized. The standard goodness-of-fit chi-square tests is shown to be admissible for systems of two or more alleles. The conditional probability distribution required to determine the exact significance level of this test is presented.

Efficiency of the determinant method of estimating gene frequencies in three allelic models.

Efficiency of three different methods: Bernstein's, maximum likelihood and determinant method were compared. A relative efficiency calculated as a ratio of variances of estimators was used for the comparison. It was shown that the determinant method is almost as efficient for estimating of recessive gene frequency as the method of maximum likelihood, and more efficient than the Bernstein's method.

Valuation of characteristics of water purity. III. The use of numerical methods for qualitative and quantitative evaluation of the degree of pollution.

The taxonometric methods of centrifugal correlation and principal components were used to classify sites along the investigated river with respect to quantity and quality of pollution. The degree of pollution was determined with the use of a collection of microbiological, hydrobiological and chemical characteristics selected by statistical methods.