Related papers: Spacing Distribution of a Bernoulli Sampled Sequen…
We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the…
In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its…
We study random points on the real line generated by the eigenvalues in unitary invariant random matrix ensembles or by more general repulsive particle systems. As the number of points tends to infinity, we prove convergence of the…
The distributions of the number of occurrences of words (the distributions of words for short) play key roles in information theory, statistics, probability theory, ergodic theory, computer science, and DNA analysis. Bassino et al. 2010 and…
The Bernoulli sieve is a random allocation scheme obtained by placing independent points with the uniform [0,1] law into the intervals made up by successive positions of a multiplicative random walk with factors taking values in the…
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…
In this paper we show the distributions of sliding block patterns for Bernoulli processes with finite alphabet, which is not based on the induction on sample size. We show a new inclusion-exclusion formula in multivariate generating…
Simultaneous perturbation stochastic approximation (SPSA) has proven to be efficient for recursive optimization. SPSA uses a centered difference approximation to the gradient based on two function evaluations regardless of the dimension of…
We consider the joint distribution of the area and perimeter statistics on the set I_n of inversion sequences of length n represented as bargraphs. Functional equations for both the ordinary and exponential generating functions are derived…
This work sheds some light on the relationship between a distribution's standard deviation and its range, a topic that has been discussed extensively in the literature. While many previous studies have proposed inequalities or relationships…
Consider the ensemble of Real Symmetric Toeplitz Matrices, each entry iidrv from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. The limiting spectral measure (the density of normalized eigenvalues)…
In this paper, we are concerned with obtaining distribution-free concentration inequalities for mixture of independent Bernoulli variables that incorporate a notion of variance. Missing mass is the total probability mass associated to the…
Extremal spacings between eigenvalues of random unitary matrices of size N pertaining to circular ensembles are investigated. Explicit probability distributions for the minimal spacing for various ensembles are derived for N = 4. We study…
Closed-form expressions for the distributions of the order statistics on the spacings between order statistics for the uniform distribution are obtained. This generalizes a result by Fisher concerning tests of significance in the harmonic…
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…
The topic of this paper is the distributed and incremental generation of long executions of concurrent systems, uniformly or more generally with weights associated to elementary actions. Synchronizing sequences of letters on alphabets…
We equip the polytope of $n\times n$ Markov matrices with the normalized trace of the Lebesgue measure of $\mathbb{R}^{n^2}$. This probability space provides random Markov matrices, with i.i.d. rows following the Dirichlet distribution of…
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…
Considering the optimal alignment of two i.i.d. random sequences of length $n$, we show that when the scoring function is chosen randomly, almost surely the empirical distribution of aligned letter pairs in all optimal alignments converges…
We calculate analytically, for finite-size matrices, joint probability densities of ratios of level spacings in ensembles of random matrices characterized by their associated confining potential. We focus on the ratios of two spacings…