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Ashot V. Kakosyan

Publications and source records attributed to Ashot V. Kakosyan.

6 recordsLinked to original sources
arXiv2024

On an arithmetical property of moments and cumulants

The main result of the paper is the following. Let a non-degenerate distribution have finite moments $μ_k$ of all orders $k=0,1,2,\ldots$. Then the sequence $\{μ_k/k!, \; k=0,1,2,\ldots\}$ either contains infinitely many different terms or at most three. In the latter case, this sequence has the form $\{1,a,1-b,a,1-b,a,1-b, \ldots\}$ and corresponds to a distribution with the characteristic function \begin{equation*}\label{ eq0} f(t)=\frac{1+iat+bt^2}{1+t^2}, \quad \text{where} \;\; b\geq 0,\; \frac{1-a-b}{2}\geq 0,\; \frac{1+a-b}{2}\geq 0. \end{equation*}.

math.PR↗
arXiv2017

Outliers and related problems

We define outliers as a set of observations which contradicts the proposed mathematical (statistical) model and we discuss the frequently observed types of the outliers. Further we explore what changes in the model have to be made in order to avoid the occurance of the outliers. We observe that some variants of the outliers lead to classical results in probability, such as the law of large numbers and the concept of heavy tailed distributions. Key words: outlier; the law of large numbers; heavy tailed distributions; model rejection.

math.PR↗
arXiv2016

Some Contra-Arguments for the Use of Stable Distributions in Financial Modeling

In the present paper, we discuss contra-arguments concerning the use of Pareto-Levý distributions for modeling in Finance. It appears that such probability laws do not provide sufficient number of outliers observed in real data. Connection with the classical limit theorem for heavy-tailed distributions with such type of models is also questionable. The idea of alternative modeling is given.

stat.AP↗
arXiv2015

On a characterization of infinitely divisible distributions with Gaussian component

We give a necessary and sufficient condition for symmetric infinitely divisible distribution to have Gaussian component. The result can be applied to approximation the distribution of finite sums of random variables. Particularly, it shows that for a large class of distributions with finite variance stable approximation appears to be better than Gaussian. keywords: infinitely divisible distributions; Gaussian component; approximations of sums of random variables.

math.PR↗