Scatter plots of multivariate data sets motivate modeling of star-shaped distributions beyond elliptically contoured ones. We study properties of estimators for the density generator function, the star-generalized radius distribution and the density...
In recent decades, the study of discrete distributions has received increasing attention in the field of statistics, mainly because discrete distributions can model a wide range of count data. One common distribution used for modeling count data, for...
In the present paper, we propose a large sample asymptotic approximation for the sampling and posterior distributions of differential entropy when the sample is composed of independent and identically distributed realization of a multivariate normal...
Statistical modeling is fundamentally based on probability distributions, which can be discrete or continuous and univariate or multivariate. This review focuses on the methods used to construct these distributions, covering both traditional and newl...
A class of power series q-distributions, generated by considering a q-Taylor expansion of a parametric function into powers of the parameter, is discussed. Its q-factorial moments are obtained in terms of q-derivatives of its series (parametric) func...
(1) Background: The distribution of tumor volumes is important for various aspects of cancer research. Unfortunately, tumor volume is rarely documented in tumor registries; usually only maximum tumor diameter is. This paper presents a method to deriv...
It is frequent for real-life count data to show inflation in lower values; however, most of the well-known count distributions cannot capture such a feature. The present paper introduces a new distribution for modeling inflated count data in small va...
Probabilistic graphical models allow us to encode a large probability distribution as a composition of smaller ones. It is oftentimes the case that we are interested in incorporating in the model the idea that some of these smaller distributions are...
In this paper, we propose a new family of distributions, by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new family of distributi...
Polynomials are common algebraic structures, which are often used to approximate functions, such as probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of systems rathe...
The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the following co...
If a message can have n different values and all values are equally probable, then the entropy of the message is log(n). In the present paper, we investigate the expectation value of the entropy, for arbitrary probability distribution. For that purpo...
The general beta of the second kind distribution (GB2) is a flexible distribution which includes several relevant parametric families of distributions. This distribution has important applications in earnings and income distributions, finance and ins...
We investigate the off-shell generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) of kaons within the framework of the Nambu–Jona-Lasinio model, employing proper time regularization. Compared to...
The Banach Gelfand Triple ( S 0 , L 2 , S 0 ′ ) ( R d ) consists of S 0 ( R d ) , ∥ · ∥ S 0 , a very specific Segal algebra as algebra of test functions, the Hilbert space...
We introduce two families of continuous distribution functions with not-necessarily symmetric densities, which contain a parent distribution as a special case. The two families proposed depend on two parameters and are presented as an alternative to...
While the total cover of broken cloud fields can in principle be obtained from one-dimensional measurements, the cloud size distribution normally differs between two-dimensional (area) and one-dimensional retrieval (chord length) methods. In this stu...
For every discrete probability distribution, there is one and only one partial summation which leaves the distribution unchanged. This invariance property is reconsidered for distributions with one parameter. We show that if we change the parameter v...
In this paper, we introduce a general family of distributions based on Whittaker function. The properties of obtained distributions, moments, ordering, percentiles, and unimodality are studied. The distributions’ parameters are estimated using...
Assume that ξ and η are two independent random variables with distribution functions Fξ and Fη, respectively. The distribution of a random variable ξη, denoted by Fξ⊗Fη, is called the product-convolution of Fξ an...
This article presents a new family of symmetric heavy-tailed distributions. This model is based on the ratio of two independent random variables; one with a normal distribution in the numerator and another with a Birnbaum–Saunders distribution...
We present a number of upper and lower bounds for the total variation distances between the most popular probability distributions. In particular, some estimates of the total variation distances in the cases of multivariate Gaussian distributions, Po...
This paper introduces a unified Bayesian approach for testing various hypotheses related to multinomial distributions. The method calculates the Kullback–Leibler divergence between two specified multinomial distributions, followed by comparing...
In this paper, we introduce the skew-symmetric generalized normal and the skew-symmetric generalized t distributions, which are skewed extensions of symmetric special cases of generalized skew-normal and generalized skew-t distributions, respectively...
The traditional linear regression model that assumes normal residuals is applied extensively in engineering and science. However, the normality assumption of the model residuals is often ineffective. This drawback can be overcome by using a generaliz...
In the framework of harmonic and Clifford analysis, specific distributions in Euclidean space of arbitrary dimension, which are of particular importance for theoretical physics, are once more thoroughly studied. Indeed, actions involving spherical co...
A new class of probability distributions closely connected to generalized hyperbolic distributions is introduced. It is better adapted for studying the distributions of sums of a random number of random variables. The properties of these distribution...
This paper provides a systematic and comprehensive treatment for obtaining general expressions of any order, for the moments and cumulants of spherically and elliptically symmetric multivariate distributions; results for the case of multivariate t-di...
A dozen papers have considered the concept of negation of probability distributions (pd) introduced by Yager. Usually, such negations are generated point-by-point by functions defined on a set of probability values and called here negators. Recently...
The Poisson regression model remains an important tool in the econometric analysis of count data. In a pioneering contribution to the econometric analysis of such models, Lung-Fei Lee presented a specification test for a Poisson model against a broad...
There are given characterizations of the exponential distribution based on the properties of independence of linear forms with random coefficients. Results based on the constancy of regression of one statistic in a linear form are obtained. Related c...
We discuss qubit-state superpositions in the probability representation of quantum mechanics. We study probability distributions describing separable qubit states. We consider entangled states on the example of a system of two qubits (Bell states) us...
In 2020, El-Morshedy et al. introduced a bivariate extension of the Burr type X generator (BBX-G) of distributions, and Muhammed presented a bivariate generalized inverted Kumaraswamy (BGIK) distribution. In this paper, we propose a more flexible gen...
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. Given that the measures were based on Shannon’s information, the novel continuous complexity measures descr...
In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate stable distributions. Multivariate analogs of the Mittag–Leffler distribution are introduced. Some properties of these...
In this article, we introduce a new family of symmetric-asymmetric distributions based on skew distributions and on the family of order statistics with proportional hazards. This new family of distributions is able to fit both unimodal and bimodal as...
In this paper, we study a new type of distribution that generalizes distributions from the gamma and beta classes that are widely used in applications. The estimators for the parameters of the digamma distribution obtained by the method of logarithmi...
Statistical modeling relies on a diverse range of statistical distributions, encompassing both univariate and multivariate distributions and/or discrete and continuous distributions. In the literature, numerous statistical methods have been proposed...
Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the finite support are pre...
The development of bivariate distributions is a challenging area of research, and a novel class of bivariate distributions is proposed in this paper. Certain useful mathematical characteristics of the proposed class of bivariate distributions are exp...
We discuss a one-parameter family of generalized cross entropy between two distributions with the power index, called the projective power entropy. The cross entropy is essentially reduced to the Tsallis entropy if two distributions are taken to be e...
In this paper, a new family of continuous distributions with positive support is introduced. This family is generated by a truncation of the family of univariate symmetrical distributions. In this new family of distributions, general properties, such...
In the paper, quasi-exponentiated normal distributions are introduced for any real power (exponent) no less than two. With natural exponents, the quasi-exponentiated normal distributions coincide with the distributions of the corresponding powers of...
Let S be a Borel subset of a Polish space and F the set of bounded Borel functions f:S→R. Let an(·)=P(Xn+1∈·∣X1,…,Xn) be the n-th predictive distribution corresponding to a sequence (Xn) of S-valued random variabl...
In the following article, a new five-parameter distribution, the alpha power exponentiated Weibull-exponential distribution is proposed, based on a newly developed technique. It is of particular interest because the density of this distribution can t...
Within the context of flexible parametric families of distributions, much work has been dedicated in recent years to the theme of skew-symmetric distributions, or symmetry-modulated distributions, as we prefer to call them. The present contribution c...
A justification of the Basel liquidity formula for risk capital in the trading book is given under the assumption that market risk-factor changes form a Gaussian white noise process over 10-day time steps and changes to P&L (profit-and-loss) are...
In this article we study basic properties of random variables X, and their associated distributions, in the second chaos, meaning that X has a representation X = ∑ k ≥ 1 λ k ( ξ k 2 − 1 ) , where ξ k &...
Mellin Transform occurs in many branches of Applied Mathematics and Engineering. The Mellin transform is very much related to the Laplace and Fourier transforms and the theory for the ordinary functions is well established. In the distributional sens...
A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, the standardized marginal distributions are standard normal. The copula itself depends on the familiar skewing construction based on the normal...
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