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Article Citation - WoS: 4Citation - Scopus: 4On the Powers of the Kummer Distribution(Academic Publication Council, 2017) Ostrovska, Sofiya; Turan, Mehmet; MathematicsThe Kummer distribution is a probability distribution, whose density is given by f (x) = cx (alpha-1)(1 + delta x)(-gamma) e(-beta x), X > 0, where alpha, beta, delta > 0, gamma is an element of R and C is a normalizing constant. In this paper, the distributions of random variable X-P, p > 0, where X has the Kummer distribution, are considered with the conditions being IFR/DFR, some properties of moments depending on the parameters and the moment-(in) determinacy. In the case of moment-indeterminacy, exemplary Stieltjes classes are constructed.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 Stieltjes Classes for Discrete Distributions of Logarithmic Type(Univ Nis, Fac Sci Math, 2020) Ostrovska, Sofiya; Turan, MehmetStieltjes classes play a significant role in the moment problem since they permit to expose explicitly an infinite family of probability distributions all having equal moments of all orders. Mostly, the Stieltjes classes have been considered for absolutely continuous distributions. In this work, they have been considered for discrete distributions. New results on their existence in the discrete case are presented.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.
