Related papers: A General size-biased distribution
We offer further results on a general size-biased distribution related to the Riemann xi-function we presented in [9] using the work of Ferrar. Curious properties associated with its expected value are presented, which are related to…
A GGC (Generalized Gamma Convolution) representation of Riemann's Xi-function is constructed.
In this paper, we derive a probability density function that generalizes the Burr XII distribution. The cumulative distribution function and the $n^{th}$ moment of the generalized distribution are obtained while the distribution of some…
Gaussian distributions can be generalized from Euclidean space to a wide class of Riemannian manifolds. Gaussian distributions on manifolds are harder to make use of in applications since the normalisation factors, which we will refer to as…
We appeal to a complex q-Fourier transform as a generalization of the (real) one analyzed in [Milan J. Math. {\bf 76} (2008) 307]. By recourse to tempered ultra-distributions we are able to show that the q-Gaussian distribution can be…
In the present article the author extends the Fourier transform to a more general class of functions; First to power-law functions with integer and half-integer exponents then to the widely used quantum statistics function (Fermi-Dirac and…
This paper provides some expansions of Riemann xi function, $\xi$, as a series of Bessel K functions.
A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a Central Limit Theorem generalized in the presence of specific correlations between the relevant random variables.…
We develop a fractional extension of the classical binomial distribution and the associated Bernstein operator, formulated within the framework of the generalized binomial theorem (Hara and Hino [Bull.\ London Math.\ Soc. \textbf{42}…
We describe positive generalized functionals in Gaussian Analysis. We focus on distribution spaces larger than the space of Hida Distributions. It is shown that a positive distribution is represented by a measure with specific growth of its…
The mathematical properties of a family of generalized beta distribution, including beta-normal, skewed-t, log-F, beta-exponential, beta-Weibull distributions have recently been studied in several publications. This paper applies these…
In this article, we study the distribution of large values of the Riemann zeta function on the 1-line. We obtain an improved density function concerning large values, holding in the same range as that given by Granville and Soundararajan.
Motivated by applications in Bayesian analysis we introduce a multidimensional beta distribution in an ordered simplex. We study properties of this distribution and connect them with the generalized incomplete beta function. This function…
In a work of Heath-Brown, it is proved that in the Pilz divisor problem, the normalized error term $\Delta_3(x)$ has a distribution function. In this paper, we prove an analogue of this result in the setting of GL(3). For a given self-dual…
The theory of Barnes beta probability distributions is advanced and related to the Riemann xi function. The scaling invariance, multiplication formula, and Shintani factorization of Barnes multiple gamma functions are reviewed using the…
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 this paper we propose an objective Bayesian estimation approach for the parameters of the generalized gamma distribution. Various reference priors are obtained, but showing that they lead to improper posterior distributions. We overcome…
The paper deals with a generalisation of uniform distribution. The analogues of Weyl's criterion are derived.
We generalize the property that Riemann sums of a continuous function corresponding to equidistant subdivision of an interval converge to the integral of that function, and we give some applications of this generalization.
We present some remarks about the embedding of spaces of Schwartz distributions into spaces of Colombeau generalized functions. We show that the various constructions of such embeddings existing in the literature lead in fact to the same…