arXiv subjects

Yurii Yurchenko

Publications and source records attributed to Yurii Yurchenko.

3 recordsLinked to original sources

arXiv2021

Foundations of abstract probability theory

Using the ideas of abstract algebra, we introduce the basic concepts of abstract probability theory that generalize the Kolmogorov's probability theory, possibility theory and other theories that deal with uncertainty. Based on abstract addition and multiplication, we define an abstract measure and abstract Lebesgue integral. System of Kolmogorov's axioms is criticized, after which we introduce an abstract probability measure and abstract conditional probability, show that they have recognizable probability properties. In addition, we define an abstract expected value operator as the abstract Lebesgue integral and prove its properties.

math.PR↗

arXiv2021

Tensor distributions with covariance tensor or correlation tensor

In this article, we define the matricization of a tensor and we present some properties of the matricization. After that, we define the determinant of a tensor and we present some properties of the determinant. We define the covariance tensor and we present some properties of the covariance tensor. In a similar way, we define the correlation tensor. We define the tensor normal distribution. In a similar way, we define the tensor elliptical distributions. We prove the equivalence of the tensor elliptical distribution representations.

math.PR↗

arXiv2021

Matrix variate and tensor variate Laplace distributions

In this article, we define a matrix variate asymmetric Laplace distribution. We prove some properties of the matrix variate asymmetric Laplace distribution. We prove the relationship between the matrix variate asymmetric Laplace distribution and other distributions. We define a matrix variate generalized asymmetric Laplace distribution. We prove some properties of the matrix variate generalized asymmetric Laplace distribution. We prove the relationship between the matrix variate generalized asymmetric Laplace distribution and other distributions. We define a tensor variate asymmetric Laplace distribution. We prove some properties of the tensor variate asymmetric Laplace distribution. We prove the relationship between the tensor variate asymmetric Laplace distribution and other distributions. We define a tensor variate generalized asymmetric Laplace distribution. We prove some properties of the tensor variate generalized asymmetric Laplace distribution. We prove the relationship between the tensor variate generalized asymmetric Laplace distribution and other distributions.

math.PR↗