Related papers: Degenerate zero-truncated Poisson random variables
We propose a novel statistical inference methodology for multiway count data that is corrupted by false zeros that are indistinguishable from true zero counts. Our approach consists of zero-truncating the Poisson distribution to neglect all…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Our main result is a proof that for sufficiently small values of the rate parameter $\lambda$,…
In this article we study the limiting empirical measure of zeros of higher derivatives for sequences of random polynomials. We show that these measures agree with the limiting empirical measure of zeros of corresponding random polynomials.…
Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and normal distributions for various functionals of the process.
By random complex zeroes we mean the zero set of a random entire function whose Taylor coefficients are independent complex-valued Gaussian variables, and the variance of the k-th coefficient is 1/k!. This zero set is distribution invariant…
In this paper we examine the deviations from Gaussianity for two types of random variable converging to a normal distribution, namely sums of random variables generated by a deterministic discrete time map and a linearly damped variable…
A new distribution named intensive natural distribution is introduced with the intent of consolidating statistics and empirical data. Based on the probability derived from the Bernoulli distribution, this method extended also Poisson…
Random models of evolution are instrumental in extracting rates of microscopic evolutionary mechanisms from empirical observations on genetic variation in genome sequences. In this context it is necessary to know the statistical properties…
In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.
Our interest is in the scaled joint distribution associated with $k$-increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifying in terms of correlation functions the same distribution…
Let $X_1,\ldots,X_M$ and $Y_1,\ldots,Y_N$ be independent zero mean normal random variables with variances $\sigma_{X_i}^2$, $i=1,\ldots,M$, and $\sigma_{Y_j}^2$, $j=1,\ldots,N$, respectively, and let $X=X_1\cdots X_M$ and $Y=Y_1\cdots Y_N$.…
Poisson thinning is an elementary result in probability, which is of great importance in the theory of Poisson point processes. In this article, we record a couple of characterization results on Poisson thinning. We also consider several…
A probabilistic approach to the study of the number of zeros of complex harmonic polynomials was initiated by W. Li and A. Wei (2009), who derived a Kac-Rice type formula for the expected number of zeros of random harmonic polynomials with…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
In this article we survey properties of mixed Poisson distributions and probabilistic aspects of the Stirling transform: given a non-negative random variable $X$ with moment sequence $(\mu_s)_{s\in\mathbb{N}}$ we determine a discrete random…
In this paper, we consider the degenerate poly-Bernoulli polynomials and present new and explicit formulas for computing them in terms of the degenerate Bernoulli polynomials and Stirling numbers of the second kind.
The trimmed mean of $n$ scalar random variables from a distribution $P$ is the variant of the standard sample mean where the $k$ smallest and $k$ largest values in the sample are discarded for some parameter $k$. In this paper, we look at…
We construct a family of random matrix models for the q-deformed Gaussian random variables G_\mu=a_\mu+a^\star_\mu where the annihilation operators a_\mu and creation operators a^\star_\nu fulfil the q-deformed commutation relation a_\mu…
In this Letter we introduce the truncated state with random coefficients (TSRC). As the coefficients of the TSRC have in principle no algorithm to produce them, our question is concerned about to what type of properties will characterize…