Related papers: On the entropy and log-concavity of compound Poiss…
Multivariate count data are commonly encountered through high-throughput sequencing technologies in bioinformatics, text mining, or in sports analytics. Although the Poisson distribution seems a natural fit to these count data, its…
In this paper we obtain the limit distribution for partial sums with a random number of terms following a class of mixed Poisson distributions. The resulting weak limit is a mixing between a normal distribution and an exponential family,…
We consider the sequential sampling of species, where observed samples are classified into the species they belong to. We are particularly interested in studying some quantities describing the sampling process when there is a new species…
Let $ V_{n} = X_{1,n} + X_{2,n} + \cdots + X_{n,n}$ where $X_{i,n}$ are Bernoulli random variables which take the value $1$ with probability $b(i;n)$. Let $\lambda_{n} = \sum\limits_{i=1}^{n} b(i;n) $, $\lambda = \lim\limits_{n \to \infty}…
The Boltzmann-Gibbs celebrated entropy $S_{BG}=-k\sum_ip_i \ln p_i$ is {\it concave} (with regard to all probability distributions $\{p_i\}$) and {\it stable} (under arbitrarily small deformations of any given probability distribution). It…
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…
We consider the approximation of a convolution of possibly different probability measures by (compound) Poisson distributions and also by related signed measures of higher order. We present new total variation bounds having a better…
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…
It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…
In this paper we show that the family P_d of probability distributions on R^d with log-concave densities satisfies a strong continuity condition. In particular, it turns out that weak convergence within this family entails (i) convergence…
We prove that, in stable families of endomorphisms of $\mathbb{P}^k(\mathbb{C})$, all invariant measures whose measure-theoretic entropy is strictly larger than $(k-1)\log d$ at a given parameter can be followed holomorphically with the…
It is well-known that assumptions of monotonicity in size-bias couplings may be used to prove simple, yet powerful, Poisson approximation results. Here we show how these assumptions may be relaxed, establishing explicit Poisson…
Asymptotically entropy of chaotic systems increases linearly and the sensitivity to initial conditions is exponential with time: these two behaviors are related. Such relationship is the analogous of and under specific conditions has been…
We consider a type of nonnormal approximation of infinitely divisible distributions that incorporates compound Poisson, Gamma, and normal distributions. The approximation relies on achieving higher orders of cumulant matching, to obtain…
Two new information-theoretic methods are introduced for establishing Poisson approximation inequalities. First, using only elementary information-theoretic techniques it is shown that, when $S_n=\sum_{i=1}^nX_i$ is the sum of the (possibly…
We investigate quantitative implications of the notion of log-concavity through a probabilistic interpretation. In particular, we derive concentration inequalities, moment and entropy bounds for random variables satisfying a precise degree…
We prove the Simons-Johnson theorem for the sums $S_n$ of $m$-dependent random variables, with exponential weights and limiting compound Poisson distribution $\CP(s,\lambda)$. More precisely, we give sufficient conditions for…
We describe five types of results concerning information and concentration of discrete random variables, and relationships between them, motivated by their counterparts in the continuous case. The results we consider are information…
We prove that certain natural random variables associated with the local eigenvalue statistics for generalized lattice Anderson models constructed with finite-rank perturbations are compound Poisson distributed. This distribution is…
Random events in space and time often exhibit a locally dependent structure. When the events are very rare and dependent structure is not too complicated, various studies in the literature have shown that Poisson and compound Poisson…