# On the accuracy of the poissonisation in the infinite occupancy scheme

@article{Chebunin2017OnTA, title={On the accuracy of the poissonisation in the infinite occupancy scheme}, author={M. Chebunin}, journal={arXiv: Probability}, year={2017} }

We obtain asymptotic accuracy of the poissonisation in the infinite occupancy scheme. All results are obtained for integer-valued random variables having a regularly varying distribution.

#### One Citation

On nested infinite occupancy scheme in random environment

- Mathematics
- 2018

We consider an infinite balls-in-boxes occupancy scheme with boxes organised in nested hierarchy, and random probabilities of boxes defined in terms of iterated fragmentation of a unit mass. We… Expand

#### References

SHOWING 1-10 OF 10 REFERENCES

Univariate approximations in the infinite occupancy scheme

- Mathematics
- 2009

The paper concerns the classical occupancy scheme with infinitely many boxes. We establish approximations to the distributions of the number of occupied boxes, and of the number of boxes containing… Expand

Small counts in the infinite occupancy scheme

- Mathematics
- 2009

The paper is concerned with the classical occupancy
scheme in which balls
are thrown independently into infinitely many
boxes, with given probability of hitting each of the boxes.
We establish… Expand

LOCAL LIMIT THEOREMS FOR FINITE AND INFINITE URN MODELS

- Mathematics
- 2008

Local limit theorems are derived for the number of occupied urns in general finite and infinite urn models under the minimum condition that the variance tends to infinity. Our results represent an… Expand

Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws ∗

- Mathematics
- 2007

This paper collects facts about the number of occupied boxes in the classical balls-in-boxes occupancy scheme with infinitely many positive frequencies: equivalently, about the number of species… Expand

Concentration inequalities in the infinite urn scheme for occupancy counts and the missing mass, with applications

- Mathematics
- 2017

An infinite urn scheme is defined by a probability mass function $(p_j)_{j\geq 1}$ over positive integers. A random allocation consists of a sample of $N$ independent drawings according to this… Expand

Functional central limit theorems for certain statistics in an infinite urn scheme

- Mathematics
- 2016

We investigate a specific infinite urn scheme first considered by Karlin (1967). We prove functional central limit theorems for the total number of urns with at least k balls for different k.

Kolmogorov Type Law of the Logarithm for Arrays

- Mathematics
- 2016

In this paper, we establish the analogue of Kolmogorov-type law of the logarithm for an array of independent random variables. The main methods are to develop the classic Bernstein’s and Kolmogorov’s… Expand

Estimation of parameters of probabilistic models which is based on the number of different elements in a sample

- Regular variation
- 2014

One - parameter probabilistic models of text statistics

- Bull . Aust . Math . Soc .