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Likelihood-based methods of statistical inference provide a useful general methodology that is appealing, as a straightforward asymptotic theory can be applied for their implementation. It is important to assess the relationships between…
In this work, we study convergence in probability and almost sure convergence for weighted partial sums of random variables that are related to the class of generalized Oppenheim expansions. It is worth noting that the random variables…
Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…
We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations…
An agglomerative clustering of random variables is proposed, where clusters of random variables sharing the maximum amount of multivariate mutual information are merged successively to form larger clusters. Compared to the previous…
We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our…
In this paper, we define the spaces $N_{\theta }^{\beta }\left( p,F,\Delta ^{m}\right) ,$ $S_{\theta }^{\beta }\left( F,\Delta ^{m}\right) ,$ $w_{p}^{\beta }\left( F,\Delta ^{m}\right) $ for sequences of fuzzy numbers using generalized…
The purpose of this paper is to define statistically convergent sequences with respect to the metrics on generalized metric spaces (g-metric spaces) and investigate basic properties of this statistical form of convergence.
In this article, we establish the mod-$\phi$ convergence of the major index of a uniform random standard tableau whose shape converges in the Thoma simplex. This implies various probabilistic estimates, in particular speed of convergence…
The concept of I-statistical convergence of sequence was first defined by Das et.al [2]. In this paper we introduce and study the notion of rough I-statistical convergence of sequence in normed linear Spaces. We also define the set of rough…
An ordinal pattern for a finite sequence of real numbers is a permutation that records the relative positions in the sequence. For random walks with steps drawn uniformly from $[-1,1]$, we show an ordinal pattern occurs with probability…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
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 extend some sharp inequalities for martingale-differences to general multiplicative systems of random variables. The key ingredient in the proofs is a technique reducing the general case to the case of Rademacher random variables without…
Convergence results for averages of independent replications of counting processes are established in a $p$-variation setting and under certain assumptions. Such convergence results can be combined with functional differentiability results…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
The concept of "stochastic precedence" between two real-valued random variables has often emerged in different applied frameworks. In this paper we consider a slightly more general, and completely natural, concept of stochastic precedence…
Consider two independent random strings having same length and taking values uniformly in a common finite alphabet. We study the order of the variance of the length of the longest common subsequences (LCS) of these strings when long blocks,…
This paper describes the probabilistic behaviour of a random Sturmian word. It performs the probabilistic analysis of the recurrence function which can be viewed as a waiting time to discover all the factors of length $n$ of the Sturmian…