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We study the convergence in distribution norms in the Central Limit Theorem for non identical distributed random variables that is $$ \varepsilon_{n}(f):={\mathbb{E}}\Big(f\Big(\frac 1{\sqrt…
Over the past decades, various methods for comparing the means of two log-normal have been proposed. Some of them are differing in terms of how the statistic test adjust to accept or to reject the null hypothesis. In this study, a new…
We have studied the parametric description of the distribution of the log-growth rates of the sizes of cities of France, Germany, Italy, Spain and the USA. We have considered several parametric distributions well known in the literature as…
Two concepts of symmetry for the distributions of positive random variables $Y$ are log-symmetry (symmetry of the distribution of $\log Y$) and R-symmetry [7]. In this paper, we characterise the distributions that have both properties,…
Testing for normality is a widely used procedure in statistics and data analysis, often applied prior to employing methods that rely on the assumption of normally distributed data. While several existing tests target distributional…
We study the generalization behavior of Markov Logic Networks (MLNs) across relational structures of different sizes. Multiple works have noticed that MLNs learned on a given domain generalize poorly across domains of different sizes. This…
The normal distribution is used as a unified probability distribution, however, our researcher found that it is not good agreed with the real-life dynamical system's data. We collected and analyzed representative naturally occurring data…
We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…
In recent years it has been increasing evidence that lognormal distributions are widespread in physical and biological sciences, as well as in various phenomena of economics and social sciences. In social sciences, the appearance of…
The size of drops generated by the capillary-driven disintegration of liquid ligaments plays a fundamental role in several important natural phenomena, ranging from heat and mass transfer at the ocean-atmosphere interface to pathogen…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
The beta normal distribution is a generalization of both the normal distribution and the normal order statistics. Some of its mathematical properties and a few applications have been studied in the literature. We provide a better foundation…
Discriminating data classes emanating from sensors is an important problem with many applications in science and technology. We describe a new transform for pattern identification that interprets patterns as probability density functions,…
Diffusion Limited Aggregation (DLA) is a model of fractal growth that was introduced in 1981 and had since attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. Despite…
Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. Various tools have been developed over the centuries to discover and study the various patterns in the sequence of…
We present Locally Orderless Networks (LON) and its theoretic foundation which links it to Convolutional Neural Networks (CNN), to Scale-space histograms, and measurement theory. The key elements are a regular sampling of the bias and the…
Many astronomical phenomena, including Fast Radio Bursts and Soft Gamma Repeaters, consist of brief, separated, seemingly aperiodic events. The intervals between these events vary randomly, but there are epochs of greater activity, with…
This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…
In the case where the dimension of the data grows at the same rate as the sample size we prove a central limit theorem for the difference of a linear spectral statistic of the sample covariance and a linear spectral statistic of the matrix…
Given $n$ samples of a regular discrete distribution $\pi$, we prove in this article first a serial of SLLNs results (of Dvoretzky and Erd\"{o}s' type) which implies a typical power law when $\pi$ is heavy-tailed. Constructing a (random)…