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Article Citation - WoS: 2Citation - Scopus: 4Constructing Stieltjes Classes for M-Indeterminate Absolutely Continuous Probability Distributions(Impa, 2014) Ostrovska, Sofiya; MathematicsIf P is a moment-indeterminate probability distribution, then it is desirable to present explicitly other distributions possessing the same moments as P. In this paper, a method to construct an infinite family of probability densities - called the Stieltjes class - all with the same moments is presented. The method is applicable for densities with support (0, infinity) which satisfy the lower bound: f(x) >= A exp{-ax(alpha)} for some A > 0, a > 0 and some alpha is an element of(0, 1/2):Article Citation - WoS: 3Citation - Scopus: 3q-stieltjes Classes for Some Families of q-densities(Elsevier Science Bv, 2019) Ostrovska, Sofiya; Turan, MehmetThe Stieltjes classes play a significant role in the moment problem allowing to exhibit explicitly infinite families of probability densities with the same sequence of moments. In this paper, the notion of q-moment determinacy/indeterminacy is proposed and some conditions for a distribution to be either q-moment determinate or indeterminate in terms of its q-density have been obtained. Also, a q-analogue of Stieltjes classes is defined for q-distributions and q-Stieltjes classes have been constructed for a family of q-densities of q-moment indeterminate distributions. (C) 2018 Elsevier B.V. All rights reserved.Article Citation - WoS: 17Citation - Scopus: 20Positive linear operators generated by analytic functions(Springer, 2007) Ostrovska, SofiyaLet phi be a power series with positive Taylor coefficients {a(k)}(k=0)(infinity) and non-zero radius of convergence r <= infinity. Let xi x, 0 <= x <= r be a random variable whose values alpha(k), k = 0, 1,..., are independent of x and taken with probabilities a(k)x(k)/phi(x), k = 0, 1,.... The positive linear operator (A(phi)f)(x) := E[f(xi x)] is studied. It is proved that if E(xi(x)) = x, E(xi(2)(x)) = qx(2) + bx + c, q, b, c is an element of R, q > 0, then A(phi) reduces to the Szasz-Mirakyan operator in the case q = 1, to the limit q-Bernstein operator in the case 0 < q < 1, and to a modification of the Lupas, operator in the case q > 1.Article Citation - WoS: 4Citation - Scopus: 4A New Proof That the Product of Three or More Exponential Random Variables Is Moment-Indeterminate(Elsevier Science Bv, 2010) Ostrovska, Sofiya; Stoyanov, JordanWe present a direct, short and transparent proof of the following result: The product X-1 ... X-n of independent exponential random variables X-1,...,X-n is moment-indeterminate if and only if n >= 3. This and other complex analytic results concerning Stieltjes moment sequences and properties of the corresponding distributions appeared recently in Berg (2005). (C) 2010 Elsevier B.V. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 2On the Powers of Polynomial Logistic Distributions(Brazilian Statistical Association, 2016) Ostrovska, SofiyaLet P(x) be a polynomial monotone increasing on (-infinity, +infinity). The probability distribution possessing the distribution function F(x) = 1/1 + exp{-P(x)} is called the polynomial logistic distribution associated with polynomial P and denoted by PL(P). It has recently been introduced, as a generalization of the logistic distribution, by V. M. Koutras, K. Drakos, and M. V. Koutras who have also demonstrated the importance of this distribution in modeling financial data. In the present paper, for a random variable X similar to PL(P), the analytical properties of its characteristic function are examined, the moment-(in)determinacy for the powers X-m, m is an element of N and vertical bar X vertical bar(p), p is an element of (0, +infinity) depending on the values of m and p is investigated, and exemplary Stieltjes classes for the moment-indeterminate powers of X are constructed.Article Citation - WoS: 1On Lin's Condition for Products of Random Variables(B verkin inst Low Temperature Physics & Engineering Nas Ukraine, 2019) Il'inskii, Alexander; Ostrovska, SofiyaThe paper presents an elaboration of some results on Lin's conditions. A new proof is given to the fact that if densities of independent random variables xi(1) and xi(2) satisfy Lin's condition, then the same is true for their product. Also, it is shown that without the condition of independence, the statement is no longer valid.Article Citation - WoS: 1Citation - Scopus: 1On Lin's Condition for Products of Random Variables With Singular Joint Distribution(Wydawnictwo Uniwersytetu Wroclawskiego, 2020) Il'inskii, Alexander; Ostrovska, SofiyaLin's condition is used to establish the moment determinacy/indeterminacy of absolutely continuous probability distributions. Recently, a number of papers related to Lin's condition for functions of random variables have appeared. In the present paper, this condition is studied for products of random variables with given densities in the case when their joint distribution is singular. It is proved, assuming that the densities of both random variables satisfy Lin's condition, that the density of their product may or may not satisfy this condition.
