Related papers: Simultaneous Joint Lower and Upper record values P…
Joint degree vectors give the number of edges between vertices of degree $i$ and degree $j$ for $1\le i\le j\le n-1$ in an $n$-vertex graph. We find lower and upper bounds for the maximum number of nonzero elements in a joint degree vector…
Here in this paper, it is tried to obtain and compare the ML estimations based on upper record values and a random sample. In continue, some theorems have been proven about the behavior of these estimations asymptotically.
Let $I=[0,1]$ and consider disjoint closed regions $G_{1},....,G_{n}$ in $% I\times I$ and subintervals $I_{1},......,I_{n},$ such that $G_{i}$ projects onto $I_{i.}$ We define the lower and upper maps $\tau_{1},$ $\tau_{2}$ by the lower…
Upper limits and confidence intervals are a convenient way to present experimental results. With modern experiments producing more and more data, it is often necessary to reduce the volume of the results for convenient distribution. A…
This paper develops upper and lower bounds for the probability of Boolean expressions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. Our technique generalizes and extends the…
Daily precipitation time series are composed of null entries corresponding to dry days and nonzero entries that describe the rainfall amounts on wet days. Assuming that wet days follow a Bernoulli process with success probability $p$, we…
We have discovered analytical expressions for the probability density function (PDF) of photons that are multiply scattered in relativistic flows, under the assumption of isotropic and inelastic scattering. These expressions characterize…
In this note, we study the set $\mathcal{D}$ of values of the quadruplet $(\underline{\mathrm{d}}(A),\overline{\mathrm{d}}(A),\underline{\mathrm{d}}(2A),\overline{\mathrm{d}}(2A))$ where $A\subset\mathbb{N}$ and…
The paper is devoted to infinite Bernoulli convolutions generated by positive multigeometric series and to probability distributions of random variables whose digits in an even integer base-$s$ expansion with two redundant digits form a…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
In this paper, we consider several types of information and methods of combination associated with incomplete probabilistic systems. We discriminate between 'a priori' and evidential information. The former one is a description of the whole…
We consider the reduced density matrix $\rho_{A}^{(m)}$ of a bipartite system $AB$ of dimensionality $mn$ in a Gaussian ensemble of random, complex pure states of the composite system. For a given dimensionality $m$ of the subsystem $A$,…
Let $p_n(y)=\sum_k\hat{\alpha}_k\phi(y-k)+\sum_{l=0}^{j_n-1}\sum_k\hat {\beta}_{lk}2^{l/2}\psi(2^ly-k)$ be the linear wavelet density estimator, where $\phi$, $\psi$ are a father and a mother wavelet (with compact support),…
Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…
We investigate determining the exact bounds of the frequencies of conjunctions based on frequent sets. Our scenario is an important special case of some general probabilistic logic problems that are known to be intractable. We show that…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
In this paper, we systematically summarize and enhance the understanding of weak convergence and functional limits of record numbers in discrete-time random walks under Spitzer's condition, and extend these findings to $\sigma$--record…
We consider two random walks evolving synchronously on a random out-regular graph of $n$ vertices with bounded out-degree $r\ge 2$, also known as a random Deterministic Finite Automaton (DFA). We show that, with high probability with…
While traditional multiple testing procedures prohibit adaptive analysis choices made by users, Goeman and Solari (2011) proposed a simultaneous inference framework that allows users such flexibility while preserving high-probability bounds…
In this paper, we define the upper (resp. lower) covariance under multiple probabilities via a corresponding max-min-max (resp. min-max-min) optimization problem and the related properties of covariances are obtained. In particular, we…