2019
Том 71
№ 10

All Issues

Petunin Yu. I.

Articles: 21
Article (Russian)

A Nonparametric Test for the Equivalence of Populations Based on a Measure of Proximity of Samples

Klyushin D. A., Petunin Yu. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 2. - pp. 147-163

We propose a new measure of proximity of samples based on confidence limits for the bulk of a population constructed using order statistics. For this measure of proximity, we compute approximate confidence limits corresponding to a given significance level in the cases where the null hypothesis on the equality of hypothetical distribution functions may or may not be true. We compare this measure of proximity with the Kolmogorov–Smirnov and Wilcoxon statistics for samples from various populations. On the basis of the proposed measure of proximity, we construct a statistical test for testing the hypothesis on the equality of hypothetical distribution functions.

Article (Russian)

Theory of quadratic estimates of variance

Petunin Yu. I., Tupko N. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 9. - pp. 1217–1231

A class of quadratic estimates is constructed for the second-order moment and variance of a random variable. These estimates are found on the basis of sample values obtained by simple sampling. The best quadratic estimates are found for the second-order moment and variance in the case of known mathematical expectation. The exactness of biased and unbiased estimates of variance is investigated in the case of unknown mathematical expectation.

Article (Russian)

Minimum-Area ellipse containing a finite set of points. II

Petunin Yu. I., Rublev В. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 8. - pp. 1098–1105

We continue the investigation of the problem of construction of a minimum-area ellipse for a given convex polygon (this problem is solved for a rectangle and a trapezoid). For an arbitrary polygon, we prove that, in the case where the boundary of the minimum-area ellipse has exactly four or five common points with the polygon, this ellipse is the minimum-area ellipse for the quadrangles and pentagons formed by these common points.

Article (Russian)

Minimum-Area ellipse containing a finite set of points. I

Petunin Yu. I., Rublev В. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 7. - pp. 980–988

From the geometric point of view, we consider the problem of construction of a minimum-area ellipse containing a given convex polygon. For an arbitrary triangle, we obtain an equation for the boundary of the minimum-area ellipse in explicit form. For a quadrangle, the problem of construction of a minimumarea ellipse is connected with the solution of a cubic equation. For an arbitrary polygon, we prove that if the boundary of the minimum-area ellipse has exactly three common points with the polygon, then this ellipse is the minimum-area ellipse for the triangle obtained.

Brief Communications (Russian)

On the concept of generalized solution of operator equations in banach spaces

Petunin Yu. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 9. - pp. 1286–1290

We introduce a new concept of generalized solution of operator equations with closed linear operator in a Banach space as an element of the completion of the space in certain locally convex topology. We prove a theorem on the existence and uniqueness of a generalized solution and give examples of finding the generalized solution for infinite systems of the linear algebraic equations.

Article (Russian)

Testing hypotheses by using optimal statistical criteria. II

Kuk Yu. V., Petunin Yu. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 5. - pp. 506–515

We study the structure of the critical function of an optimal statistical criterion for testing an arbitrary finite set of simple alternative hypotheses.

Article (Russian)

Testing hypotheses by using optimal statistical criteria. I

Kuk Yu. V., Petunin Yu. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 378–388

We propose a method for constructing statistical criteria. It can be used for testing an arbitrary finite set of simple alternative hypotheses. A concept of an optimal statistical criterion is introduced, special cases of which are the Bayesian criterion and the minimax criterion. It is proved that any optimal statistical criterion can be constructed on the basis of the likelihood ratio.

Article (Ukrainian)

A generalization of Bernoulli's model occurring in order statistics II

Matveichuk S. A., Petunin Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 6. - pp. 779-786

Article (Ukrainian)

A generalization of the Bernoulli model occurring in order statistics. I.

Matveichuk S. A., Petunin Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 4. - pp. 518–528

Article (Ukrainian)

Continuity of maps inverse to quadratic operator polynomials

Petunin Yu. I., Savkin V. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 11. - pp. 1512–1521

Article (Ukrainian)

Convergence generated by analytic functionals, and isomorphism of algebras of analytic functions

Petunin Yu. I., Savkin V. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 6. - pp. 799–803

Article (Ukrainian)

Questions on imbedding quotient spaces and Banach algebras

Petunin Yu. I., Pogrebnoy V. D.

Full text (.pdf)

Ukr. Mat. Zh. - 1985. - 37, № 1. - pp. 87 – 93

Article (Ukrainian)

Characterization of the Hilbert space L2 (Ω, U, μ) in terms of the additivity of the measure of dispersion

Baidak G. I., Braverman M. Sh., Petunin Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1984. - 36, № 6. - pp. 683 – 688

Article (Ukrainian)

Classification of stationary stochastic processes

Kuritsyn Yu. G., Petunin Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1982. - 34, № 3. - pp. 374—377

Article (Ukrainian)

Topological imbedding of semiordered topological vector spaces

Petunin Yu. I., Pogrebnoy V. D.

Full text (.pdf)

Ukr. Mat. Zh. - 1977. - 29, № 3. - pp. 344–350

Article (Ukrainian)

Linear regression parameter estimation in the presence of constraints on linear regression coefficients

Kuk Yu. V., Petunin Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1976. - 28, № 4. - pp. 463–472

Article (Ukrainian)

A new method to construct estimates for the coefficients of a linear regression

Kuk Yu. V., Petunin Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1976. - 28, № 2. - pp. 237–243

Article (Ukrainian)

On the structure of a ?-algebra of borel sets and the convergence of certain stochastic series in Banach spaces

Buldygin V. V., Petunin Yu. I., Shneyberg M. Ya.

Full text (.pdf)

Ukr. Mat. Zh. - 1975. - 27, № 4. - pp. 435–442

Article (Ukrainian)

Some properties of the set of functionals which attain their supremum on the unit sphere

Petunin Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1974. - 26, № 1. - pp. 102–106

Article (Ukrainian)

Asymptotic behavior of variance of best unbiased linear estimate of unknown mean of stationary random process obtained by uniform division of observation interval

Kuk Yu. V., Petunin Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1973. - 25, № 2. - pp. 214—227

Article (Ukrainian)

Interpolation between factor spaces

Petunin Yu. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1971. - 23, № 2. - pp. 157–167