Related papers: Runs in Random Sequences over Ordered Sets
Order statistics find applications in various areas of communications and signal processing. In this paper, we introduce an unified analytical framework to determine the joint statistics of partial sums of ordered random variables (RVs).…
We propose results of the investigation of properties of the random sums of random variables. We consider the case, where the number of summands is the first moment of an event occurrence. An integral equation is presented that determines…
We give recurrences, generating functions and explicit exact expressions for the enumeration of fundamental quantities involving runs in binary strings. We first focus on enumerations concerning runs of ones, and we then analyse the same…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and…
Given a countably infinite group $G$ acting on some space $X$, an increasing family of finite subsets $G_n$ and $x\in X$, a natural question to ask is what asymptotical distribution the sets $G_nx$ form. More formally, we define for a…
In this paper we study finite velocity planar random motions with an infinite number of possible directions, where the number of changes of direction is randomized by means of an inhomogeneous fractional Poisson distribution. We first…
A random graph order is a partial order achieved by independently sprinkling relations on a vertex set (each with probability $p$) and adding relations to satisfy the requirement of transitivity. A \textit{post} is an element in a partially…
Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action…
A graph generative model defines a distribution over graphs. One type of generative model is constructed by autoregressive neural networks, which sequentially add nodes and edges to generate a graph. However, the likelihood of a graph under…
We study probability distributions of convergent random series of a special structure, called perpetuities. By giving a new argument, we prove that such distributions are of pure type: degenerate, absolutely continuous, or continuously…
We present explicit formulae for parameterized families of probabilities of the number of nonoverlapping words and increasing nonoverlapping words in independent and identically distributed (i.i.d.) finite valued random variables,…
We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also consider a random interval partial order on $n$ elements,…
We determine the probability distribution for relative projective objects in an exceptional sequence of type $A_n$ of any length. We show that these events (the $j$-th object in an exceptional sequence of length $k\le n$ being relatively…
We present an algorithmic approach to estimate the value distributions of random variables of probabilistic loops whose statistical moments are (partially) known. Based on these moments, we apply two statistical methods, Maximum Entropy and…
In the late 1970s, C.A. Petri introduced partially ordered event occurrences (runs), then called \emph{processes}, as the appropriate model to describe the individual evolutions of distributed systems. Here, we present a unified framework…
We introduce the notion of a random mean generated by a random variable and give a construction of its expected value. We derive some sufficient conditions under which strong laws of large numbers and some limit theorems hold for random…
A permutation $\sigma$ describing the relative orders of the first $n$ iterates of a point $x$ under a self-map $f$ of the interval $I=[0,1]$ is called an \emph{order pattern}. For fixed $f$ and $n$, measuring the points $x\in I$ (according…
In this paper, we study a distribution of labeled particles on a continuous ring. It arises in three different ways, all related to the multi-type TASEP on a ring. We prove formulas for the probability density function for some permutations…
We study random number generators (RNGs), both in the fixed to variable-length (FVR) and the variable to fixed-length (VFR) regimes, in a universal setting in which the input is a finite memory source of arbitrary order and unknown…