Related papers: Random means generated by random variables: expect…
A random walk generated by a sum of independent identity distributed random variables with positive expectation is considered. The limiting distributions for the first- passage -time of a step-function boundary are derived.
In this paper is proved the limit theorem for randomly indexed sequence of random processes in the case where sequences of random index and random processes are independent, also the estimation of convergence rate is obtained.
Researchers have demonstrated that humans are unable to generate a sequence of random numbers that corresponds in a statistical sense to a simple distribution such as the uniform distribution. The purpose of this article is to present the…
We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most…
In this paper, on the sublinear expectation space, we establish a comparison theorem between independent and convolutionary random vectors, which states that the partial sums of those two sequences of random vectors are identically…
For a large class of statistical systems a geometric mean value of the observables is constrained. These observables are characterized by a power-law statistical distribution.
We define a random zonotope in Euclidean space, by adding finitely many random segments, which are independently and identically distributed. For this random polytope, we determine, under a mild assumption on the distribution, the…
In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently…
We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner growth setting, including specific cases of dependence amongst the summands and summands with heavy…
In this paper we introduce randomized $t$-type statistics that will be referred to as randomized pivots. We show that these randomized pivots yield central limit theorems with a significantly smaller magnitude of error as compared to that…
We study a generalization of the Random Energy Model to the case when the number of exponential factors varies at random. Also a relation between REM and the Erd"os-R'enyi limit theorem for maximums of partial sums is considered.
We determine the distributions of lengths of runs in random sequences of elements from a totally ordered set (total order) or partially ordered set (partial order). In particular, we produce novel formulae for the expected value, variance,…
In Part I of this article (Banerjee and Kuchibhotla (2023)), we have introduced a new method to bound the difference in expectations of an average of independent random vector and the limiting Gaussian random vector using level sets. In the…
We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite…
We establish a central limit theorem for the eigenvalue counting function of a matrix of real Gaussian random variables.
We derive new bounds of the remainder in a combinatorial central limit theorem without assumptions on independence and existence of moments of summands. For independent random variables our theorems imply Esseen and Berry-Esseen type…
Using an averaged generating function for coloured hard-dimers, some random variables of interest are studied. The main result lies in the fact that all their probability distributions obey a central limit theorem.
This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…
In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.