Related papers: Applications of certain probability distributions …
One may consider the generalization of Jacobi polynomials and the Jacobi function of the second kind to a general function where the index is allowed to be a complex number instead of a non-negative integer. These functions are referred to…
The purpose of this article has two fold. The first is to generalize some recent second main theorems for the mappings and moving hyperplanes of $\P^n(\C)$ to the case where the counting functions are truncated multiplicity (by level $n$)…
Let a ``complex probability'' be a normalizable complex distribution $P(x)$ defined on $\R^D$. A real and positive probability distribution $p(z)$, defined on the complex plane $\C^D$, is said to be a positive representation of $P(x)$ if…
Generalizations to the permutation test are introduced to allow for situations in which the null model is not exchangeable. It is shown that the generalized permutation tests are exact, and a partial converse: that any test function that is…
In this article, for modelling numeral systems, the operator approach, which is introduced in [25], is generalized for a certain case. An example of such numeral systems is introduced and considered.
This thesis presents a series of theoretical results and practical realisations about the theory of computation in distributive categories. Distributive categories have been proposed as a foundational tool for Computer Science in the last…
This paper has several major purposes. The central purpose is to describe the "Benford analysis" of a positive random variable and to summarize some results from investigations into base dependence of Benford random variables. The principal…
Application of the exact statistical inference frequently leads to a non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by…
The main aim of the present work is to arrive at a mathematical theory close to the historically original conception of generalized functions, i.e. set theoretical functions defined on, and with values in, a suitable ring of scalars and…
We provide examples of multiplicative functions $f$ supported on the $k$-free integers such that at primes $f(p)=\pm 1$ and such that the partial sums of $f$ up to $x$ are $o(x^{1/k})$. Further, if we assume the Generalized Riemann…
The article is devoted to introduce and investigation of new numeral systems. These representations are generalizations of classical representations of real numbers. The main properties of investigating representations are described. The…
This is mainly a small exposition on extensions of valuation rings as a filtered union of smooth algebras.
We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the…
This paper studies the probabilistic function approximation problem over reproducing kernel Hilbert spaces. We show the existence and uniqueness of the optimizer under mild assumptions. Furthermore, we generalize the celebrated representer…
Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…
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…
In this paper we establish a number of new estimates concerning the prime counting function \pi(x), which improve the estimates proved in the literature. As an application, we deduce a new result concerning the existence of prime numbers in…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
The paper deals with three generalized dependent setups arising from a sequence of Bernoulli trials. Various distributional properties, such as probability generating function, probability mass function and moments are discussed for these…
We describe Bayes factors functions based on the sampling distributions of \emph{z}, \emph{t}, $\chi^2$, and \emph{F} statistics, using a class of inverse-moment prior distributions to define alternative hypotheses. These non-local…