相关论文: Monotonicity properties of the Poisson approximati…

It is well known that a binomial $(n,p)$ can be approximated by a Poisson distribution with parameter $np$. The typical approach in undergraduate probability texts is to show a convergence result for the distribution of the binomial as $n$…

Compound Poisson distributions and signed compound Poisson measures are used for approximation of the Markov binomial distribution. The upper and lower bound estimates are obtained for the total variation, local and Wasserstein norms. In a…

The field of property testing of probability distributions, or distribution testing, aims to provide fast and (most likely) correct answers to questions pertaining to specific aspects of very large datasets. In this work, we consider a…

In this article, we define a matrix multinomial distribution. We prove some properties of the matrix multinomial distribution. We prove that the matrix Poisson distribution can be used as an approximation to the matrix multinomial…

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…

We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…

The idea behind Poisson approximation to the binomial distribution was used in [J. de la Cal, F. Luquin, J. Approx. Theory, 68(3), 1992, 322-329] and subsequent papers in order to establish the convergence of suitable sequences of positive…

A Poisson Binomial distribution over $n$ variables is the distribution of the sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we have…

A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…

The empirical probability density function for the conditional distribution of the true value of Poisson distribution parameter on one measurement is constructed by computer experiment. The analysis of the obtained distributions confirms…

In this note we discuss additional properties of mixed Poisson distributions. We discuss the convergence of mixed Poisson distributions to its mixing distribution for the scaling parameter tending to infinity. Moreover, we obtain a central…

From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop…

This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the…

In this article, we obtain, for the total variance distance, the error bounds between Poisson and convolution of power series distributions via Stein's method. This provides a unified approach to many known discrete distributions. Several…

We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well. We do not restrict…

One aspect of Poisson approximation is that the support of the random variable of interest is often finite while the support of the Poisson distribution is not. In this paper we will remedy this by examining truncated negative binomial (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 $\lambda$,…

The Conway-Maxwell-Poisson (CMP) distribution is a natural two-parameter generalisation of the Poisson distribution which has received some attention in the statistics literature in recent years by offering flexible generalisations of some…

Let $b(x)$ be the probability that a sum of independent Bernoulli random variables with parameters $p_1, p_2, p_3, \ldots \in [0,1)$ equals $x$, where $\lambda := p_1 + p_2 + p_3 + \cdots$ is finite. We prove two inequalities for the…

We consider Kemp's q-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established. Some of them are q-analogues of…