Partial-sums probability distributions: limits, oscillations, bivariate generalizations
Lívia Rosová
PhD thesis advisor:
Ján Mačutek
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PhD thesis - Full text 
Abstract:
Partial summations of probability distributions have been studied so far mainly for the one-dimensional
case, where one probability distribution called a parent is transformed into
another probability distribution called a descendant by a summation. In this work, we
first investigate several specific cases of one-dimensional partial summations. The next chapters focus
on two-dimensional partial summations. Specifically,
we derive relations between the probability generating functions and moments of the parent
and the descendant. We formulate a necessary and sufficient condition for invariance
of the partial summations (conditions under which the parent is identical with the descendant).
We also examine the sequences of the distributions created by iterated partial sums,
restricting ourselves to distributions with a finite support.
References
[1] Leššová L., Mačutek J. (2020): On the limit behaviour of finite-support bivariate discrete probability distributions under iterated partial summations, Acta Mathematica Universitatis Comenianae, to appear.
[2] Leššová, L. (2019): Oscillating sequences of partial-sums discrete probability distributions. Proceedings from the 21st European Young Statisticians Meeting, Milošević B. and Obradović, M. editors, Faculty of Mathematics, Belgrade, pp. 41-45.