Related papers: Compound Bi-free Poisson Distributions
In this paper, we establish a sufficient condition to compare linear combinations of independent and identically distributed (iid) infinite-mean random variables under usual stochastic order. We introduce a new class of distributions that…
We study the distribution of spacings between squares modulo q, where q is square-free and highly composite, in the limit as the number of prime factors of q goes to infinity. We show that all correlation functions are Poissonian, which…
We use the Stein-Chen method to obtain compound Poisson approximations for the distribution of the number of subgraphs in a generalised stochastic block model which are isomorphic to some fixed graph. This model generalises the classical…
We study statistical signatures of composite bosons made of two fermions using a new many-body approach. Extending number-states to composite bosons, two-particle correlations as well as the dispersion of the probability distribution are…
In this article the relation between the tail behaviours of a free regular infinitely divisible (positively supported) probability measure and its L\'evy measure is studied. An important example of such a measure is the compound free…
A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials,…
This note shows that the matrix forms of several one-parameter distribution families satisfy a hierarchical low-rank structure. Such families of distributions include binomial, Poisson, and $\chi^2$ distributions. The proof is based on a…
Using the LePage representation, a strictly stable random element in a Banach space with $\alpha\in(0,2)$ can be represented as a sum of points of a Poisson process. This point process is union-stable, i.e. the union of its two independent…
In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.
We prove some general results about the asymptotics of the distribution of the number of cycles of given length of a random permutation whose distribution is invariant under conjugation. These results were first established to be applied in…
In this article, we propose a new three parameter distribution by compounding negative binomial with reciprocal inverse Gaussian model called negative binomial-reciprocal inverse Gaussian distribution. This model is tractable with some…
Heavy-tailed random variables have been used in insurance research to model both loss frequencies and loss severities, with substantially more emphasis on the latter. In the present work, we take a step toward addressing this imbalance by…
The two-parameter Poisson-Dirichlet diffusion takes values in the infinite ordered simplex and extends the celebrated infinitely-many-neutral-alleles model, having a two-parameter Poisson-Dirichlet stationary distribution. Here we identify…
We introduce the free analogue of the classical beta prime distribution by the multiplicative free convolution of the free Poisson and the reciprocal of free Poisson distributions, and related free analogues of the classical $F$, $T$, and…
Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
We study the analogue of Kummer distribution in free probability. We prove characterization of free-Kummer and free Poisson distributions by freeness properties together with some assumptions about conditional moments. Our main tools are…
Let $X_1,X_2,...,X_n$ be a sequence of independent or locally dependent random variables taking values in $\mathbb{Z}_+$. In this paper, we derive sharp bounds, via a new probabilistic method, for the total variation distance between the…
We present analogues of the Poisson limit distribution for the noncommutative bm-independence, which is associated with several positive symmetric cones. We construct related discrete Fock spaces with creation, annihilation and conservation…
In this paper, we propose a discrete circular distribution obtained by extending the wrapped Poisson distribution. This new distribution, the Invariant Wrapped Poisson (IWP), enjoys numerous advantages: simple tractable density,…