Related papers: Asymptotic distributions for a class of generalize…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are developed.
In this manuscript we introduce a generalisation of the log-Normal distribution that is inspired by a modification of the Kaypten multiplicative process using the $q$-product of Borges [Physica A \textbf{340}, 95 (2004)]. Depending on the…
We consider the marginal models of Liang and Zeger [Biometrika 73 (1986) 13-22] for the analysis of longitudinal data and we develop a theory of statistical inference for such models. We prove the existence, weak consistency and asymptotic…
Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…
Superstatistics are superpositions of different statistics relevant for driven nonequilibrium systems with spatiotemporal inhomogeneities of an intensive variable (e.g., the inverse temperature). They contain Tsallis statistics as a special…
We obtain in this paper a non-asymptotic non-improvable up to multiplicative constant moment and exponential tail estimates for distribution for U-statistics by means of martingale representation. We show also the exactness of obtained…
The Stirling permutations introduced by Gessel-Stanley have recently received considerable attention. Motivated by Ji's work on $(\alpha,\beta)$-Eulerian polynomials (Sci China Math., 2025) and Yan-Yang-Lin's work on $1/k$-Eulerian…
Our goal is to develop a general strategy to decompose a random variable $X$ into multiple independent random variables, without sacrificing any information about unknown parameters. A recent paper showed that for some well-known natural…
In this paper, we consider a coherent theory about the asymptotic representations for a family of inequality indices called Theil-Like Inequality Measures (TLIM), within a Gaussian field. The theory uses the functional empirical process…
The aim of this note is to announce some results about the probabilistic and deterministic asymptotic properties of linear groups. The first one is the analogue, for norms of random matrix products, of the classical theorem of Cramer on…
In this paper, we present the asymptotic distribution of M-estimators for parameters in non-stationary AR(p) processes. The innovations are assumed to be in the domain of attraction of a stable law with index $0<\alpha\le2$. In particular,…
The standard A/B testing approaches are mostly based on t-test in large scale industry applications. These standard approaches however suffers from low statistical power in business settings, due to nature of small sample-size or…
The Conway-Maxwell-Poisson distribution is a two-parameter generalisation of the Poisson distribution that can be used to model data that is under- or over-dispersed relative to the Poisson distribution. The normalizing constant…
We study the Euler-Frobenius numbers, a generalization of the Eulerian numbers, and the probability distribution obtained by normalizing them. This distribution can be obtained by rounding a sum of independent uniform random variables; this…
The aim of this article is to establish asymptotic distributions and consistency of subsampling for spectral density and for magnitude of coherence for non-stationary, almost periodically correlated time series. We show the asymptotic…
We consider the \mnk{classical} problem of a controller activating (or sampling) sequentially from a finite number of $N \geq 2$ populations, specified by unknown distributions. Over some time horizon, at each time $n = 1, 2, \ldots$, the…
A statistic can be a function of multiple samples. There is little existing work on asymptotic theory for such statistics when group membership is random. We propose a flexible framework that can handle both deterministic and random…
Generalized likelihoods are commonly used to obtain consistent estimators with attractive computational and robustness properties. Formally, any generalized likelihood can be used to define a generalized posterior distribution, but an…
By application of the theory for second-order linear differential equations with two turning points developed in [Olver F.W.J., Philos. Trans. Roy. Soc. London Ser. A 278 (1975), 137-174], uniform asymptotic approximations are obtained in…