Browsing by Author "Khalleefah, Mohammed Ahmed Saad"
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Item STIELTJES CLASSES FOR KUMMER TYPE PROBABILITY DISTRIBUTIONS(2022-02-21) Khalleefah, Mohammed Ahmed Saad; Ostrovska, Sofiya; Turan, MehmetThe moment problem is one of the classical directions in Probability Theory, which studies whether or not a probability distribution is uniquely determined by its mo ments. The problem originated in XIX century and is still drawing attention of re searches both in mathematics and applied disciplines. During the last decades, the subject of finding families of different probability distributions with the same mo ment sequences has gained a popularity and a large number of papers in this area has been published. Special classes of such families, called the Stieltjes classes, have become an area of intensive research. In this thesis, after background information on the transform methods, a review of both classical and present-day results on the moment problems is presented. The re view includes a general description of the moment problem, a list of checkable criteria for the moment (in)determinacy, and some methods to construct Stieltjes classes for probability densities. All notions and results are illustrated by examples. In addition, recently introduced power Lindley distribution has been studied and new Stieltjes classes for the power Lindley density has been constructed.