Related papers: Bicomplex Mittag-Leffler Distribution
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin…
The properties of Mittag-Leffler function is reviewed within the framework of an umbral formalism. We take advantage from the formal equivalence with the exponential function to define the relevant semigroup properties. We analyse the…
We calculate moments and moment generating functions of two distributions: the so called $q-$Normal and the so called conditional $q-$Normal distributions. These distributions generalize both Normal ($q=1),$ Wigner ($% q=0,$ $q-$Normal) and…
The statistical parameters of five generalizations of the Lindley distribution, such as the average, variance and moments, are reviewed. A new double truncated Lindley distribution with three parameters is derived. The new distributions are…
In this article, we proposed a new probability distribution named as power Maxwell distribution (PMaD). It is another extension of Maxwell distribution (MaD) which would lead more flexibility to analyze the data with non-monotone failure…
We study a class of positive random variables having moments of Gamma type, whose density can be expressed by the three-parametric Mittag-Leffler functions. We give some necessary conditions and some sufficient conditions for their…
We quantify the elementary Borel-Cantelli Lemma by higher moments of the overlap count statistic in terms of the weighted summability of the probabilities. Applications include mean deviation frequencies in the Strong Law and the Law of the…
The class of Riemann zeta distribution is one of the classical classes of probability distributions on R. Multidimensional Shintani zeta function is introduced and its definable probability distributions on R^d are studied. This class…
In this pedagogical text aimed at those wanting to start thinking about or brush up on probabilistic inference, I review the rules by which probability distribution functions can (and cannot) be combined. I connect these rules to the…
This paper first surveys the connection of integrable systems of the Painleve type to various distribution functions appearing in Wigner-Dyson random matrix theory. A short discussion is then given of the appearance of these same…
Likelihood functions are ubiquitous in data analyses at the LHC and elsewhere in particle physics. Partly because "probability" and "likelihood" are virtual synonyms in everyday English, but crucially distinct in data analysis, there is…
We introduce a new class of multiplications of distributions in one dimension merging together two different regularizations of distributions. Some of the features of these multiplications are discussed in a certain detail. We use our…
The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback--Leibler from the normal and half normal distributions are approximated using…
The family of Boltzmann distributions is used in statistical mechanics to describe the distribution of states in systems with a given temperature. We give a novel characterization of this family as the unique one satisfying independence for…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
A two--step Christoffel function based solution is proposed to distribution regression problem. On the first step, to model distribution of observations inside a bag, build Christoffel function for each bag of observations. Then, on the…
The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…
Two approximations are frequently used in statistical physics: the first one, which we shall name the mean values approximation, is generally (and improperly) named as "maximum term approximation". The second is the "Stirling…
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…