Related papers: Symmetric generalized binomial distributions
Consider an election where N seats are distributed among parties with proportions p_1,...,p_m of the votes. We study, for the common divisor and quota methods, the asymptotic distribution, and in particular the mean, of the seat excess of a…
We show that various identities from [1] and [3] involving Gould-Hopper polynomials can be deduced from the real but also complex orthogonal invariance of multivariate Gaussian distributions. We also deduce from this principle a useful…
Bayesian tests on the symmetry of the generalized von Mises model for planar directions (Gatto and Jammalamadaka, 2007) are introduced. The generalized von Mises distribution is a flexible model that can be axially symmetric or asymmetric,…
We study global distribution of zeros for a wide range of ensembles of random polynomials. Two main directions are related to almost sure limits of the zero counting measures, and to quantitative results on the expected number of zeros in…
In nature or societies, the power-law is present ubiquitously, and then it is important to investigate the mathematical characteristics of power-laws in the recent era of big data. In this paper we prove the superposition of non-identical…
A celebrated analogy between prime factorizations of integers and cycle decompositions of permutations is explored here. Asymptotic formulas characterizing semismooth numbers (possessing at most several large factors) carry over to random…
In this paper, algorithms are developed for computing the Stirling transform and the inverse Stirling transform; specifically, we investigate a class of sequences satisfying a two-term recurrence. We derive a general identity which…
On the basis of integral representations of Poisson and binomial distribution functions via complete and incomplete Euler \Gamma- and B-functions, we introduce and discuss continuous counterparts of the Poisson and binomial distributions.…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
We consider and reformulate a recent definition of multiplication between distributions. We show that this definition can be adopted, in particular, to prove biorthonormality of some distributions arising when looking to the (generalized)…
Generalized L\"uroth series generalize $b$-adic representations as well as L\"uroth series. Almost all real numbers are normal, but it is not easy to construct one. In this paper, a new construction of normal numbers with respect to…
Available in the literature are properties which characterize the gamma distribution via independence of two appropriately chosen statistics. Well-known is the classical result when one of the statistics is the sample mean and the other one…
Accurately forecasting the probability distribution of phenomena of interest is a classic and ever more widespread goal in statistics and decision theory. In comparison to point forecasts, probabilistic forecasts aim to provide a more…
A signed probability distribution may extend a given traditional probability from observable events to all events. We formalize and illustrate this approach. We also illustrate its limitation. We argue that the right question is not what…
We present a relationship between the generalized hyperharmonic numbers and the poly-Bernoulli polynomials, motivated from the connections between harmonic and Bernoulli numbers. This relationship yields numerous identities for the…
We argue that negative skew and positive mean of the distribution of stock returns are largely due to the broken symmetry of stochastic volatility governing gains and losses. Starting with stochastic differential equations for stock returns…
This paper proposes another constant that can be associated with Fibonacci sequence. In this work, we look at the probability distributions generated by the linear convolution of Fibonacci sequence with itself, and the linear convolution of…
A weight-dependent generalization of the binomial theorem for noncommuting variables is presented. This result extends the well-known binomial theorem for q-commuting variables by a generic weight function depending on two integers. For a…
Associated to each random variable $Y$ having a finite moment generating function, we introduce a different generalization of the Stirling numbers of the second kind. Some characterizations and specific examples of such generalized numbers…
In this technical report, we will make two observations concerning symmetries of the probability distribution resulting from projection of a piece of p-dimensional data onto a random m-dimensional subspace of $\mathbb{R}^p$, where m < p. In…