Kolmogorov bounds for decomposable random variables and subgraph counting by the Stein–Tikhomirov method

On the bounds in Poisson approximation for independent geometric distributed random variables

‎The main purpose of this note is to establish some bounds in Poisson approximation for row-wise arrays of independent geometric distributed random variables using the operator method‎. ‎Some results related to random sums of independent geometric distributed random variables are also investigated.

Kolmogorov Random Graphs and the Incompressibility Method

We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance of the number of (possibly overlapping) ordered labeled subgraphs of a labeled graph as a function of its randomness deficiency (how far it falls short of t...

The Equilibrium Distribution of Counting Random Variables

We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop—loss transform and the mean residual lifetime, are derived. Expressions are obtained for higher order equilibrium distribution functions under mixtures and convolutions of a counting distribution. Recursive formulas for higher order equilibri...

Bounds for CDFs of Order Statistics Arising from INID Random Variables

In recent decades, studying order statistics arising from independent and not necessary identically distributed (INID) random variables has been a main concern for researchers. A cumulative distribution function (CDF) of these random variables (Fi:n) is a complex manipulating, long time consuming and a software-intensive tool that takes more and more times. Therefore, obtaining approximations a...

Bounds for the Regularity of Edge Ideal of Vertex Decomposable and Shellable Graphs