Asymptotics of Poisson approximation to random discrete distributions: an analytic approach

نویسنده

  • Hsien-Kuei Hwang
چکیده

Poisson approximation has received extensive interest in recent probability literature. The general problem is to derive bounds on the closeness of a suitable Poisson distribution to the distribution in question (usually of discrete type). To measure the degree of proximity of Poisson approximation, the following distances are usually introduced: for any two random variables X and Y taking values in the set of nonnegative integers

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A continuous approximation fitting to the discrete distributions using ODE

The probability density functions fitting to the discrete probability functions has always been needed, and very important. This paper is fitting the continuous curves which are probability density functions to the binomial probability functions, negative binomial geometrics, poisson and hypergeometric. The main key in these fittings is the use of the derivative concept and common differential ...

متن کامل

A new approach to Poisson approximation and applications

The main purpose of this article is to introduce a new approach to Poisson approximation. Some bounds in Poisson approximation for probability distributions of a wide class of various arrays of row-wise independent discrete random variables are established via a probability distance. Some analogous results related to random sums in Poisson approximation are also considered.

متن کامل

Spatial count models on the number of unhealthy days in Tehran

Spatial count data is usually found in most sciences such as environmental science, meteorology, geology and medicine. Spatial generalized linear models based on poisson (poisson-lognormal spatial model) and binomial (binomial-logitnormal spatial model) distributions are often used to analyze discrete count data in which spatial correlation is observed. The likelihood function of these models i...

متن کامل

Total Variation Asymptotics for Sums of Independent Integer Random Variables

Let $W_n := \sum_{j=1}^n Z_j$ be a sum of independent integer-valued random variables. In this paper, we derive an asymptotic expansion for the probability $\mathbb{P}[W_n \in A]$ of an arbitrary subset $A \in \mathbb{Z}$. Our approximation improves upon the classical expansions by including an explicit, uniform error estimate, involving only easily computable properties of the distributions of...

متن کامل

Asymptotic variance of random symmetric digital search trees

Asymptotics of the variances of many cost measures in random digital search trees are often notoriously messy and involved to obtain. A new approach is proposed to facilitate such an analysis for several shape parameters on random symmetric digital search trees. Our approach starts from a more careful normalization at the level of Poisson generating functions, which then provides an asymptotica...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1998