# Rates of convergence towards the Frechet distribution

@article{Bartholme2013RatesOC, title={Rates of convergence towards the Frechet distribution}, author={Carine Bartholm'e and Yvik Swan}, journal={arXiv: Probability}, year={2013} }

We develop Stein's method for the Frechet distribution and apply it to com- pute rates of convergence in distribution of renormalized sample maxima to the Frechet distribution.

## 7 Citations

### Remark on rates of convergence to extreme value distributions via the Stein equations

- Mathematics
- 2020

Consider the maximum of independent and identically distributed random variables. The classical result says that the renormalized sample maximum converges to an extreme value distributions, under…

### RATE OF CONVERGENCE TOWARD THE FREE EXTREME VALUE DISTRIBUTIONS VIA THE STEIN’S METHOD

- Mathematics
- 2021

Let {Xn}n be a sequence of freely independent, identically distributed non-commutative random variables. Consider a sequence {Wn}n of the renormalized maximum of random variables X1, · · · , Xn. It…

### Rates of convergence for laws of the spectral maximum of free random variables

- Mathematics
- 2021

Let {Xn}n be a sequence of freely independent, identically distributed non-commutative random variables. Consider a sequence {Wn}n of the renormalized spectral maximum of random variables X1, · · · ,…

### Information-theoretic convergence of extreme values to the Gumbel distribution

- Mathematics, Computer ScienceArXiv
- 2020

It is shown that, assuming certain properties of the von Mises representation, convergence to the Gumbel can be proved in the strong sense of relative entropy, and a new type of score function is introduced which behaves well under the maximum operation.

### Stein's method for comparison of univariate distributions

- Mathematics
- 2014

We propose a new general version of Stein's method for univariate distributions. In particular we propose a canonical definition of the Stein operator of a probability distribution {which is based on…

### Approximate Computation of Expectations: the Canonical Stein Operator

- Mathematics
- 2014

We propose a canonical definition of the Stein operator and Stein class of a distribution. The resulting Stein identity highlights the unifying theme behind the literature on Stein's method. Viewing…

## References

SHOWING 1-10 OF 12 REFERENCES

### Rates of Convergence for Densities in Extreme Value Theory

- Mathematics
- 1988

On donne un resultat de taux de convergence pour la densite de maxima d'echantillons normalises vers la densite limite appropriee

### Uniform rates of convergence in extreme-value theory

- MathematicsAdvances in Applied Probability
- 1982

Rates of convergence are derived for the convergence in distribution of renormalised sample maxima to the appropriate extreme-value distribution. Related questions which are discussed include the…

### Normal Approximation by Stein ’ s Method

- Mathematics
- 2003

The aim of this paper is to give an overview of Stein’s method, which has turned out to be a powerful tool for estimating the error in normal, Poisson and other approximations, especially for sums of…

### Stein’s density approach and information inequalities

- Mathematics, Computer Science
- 2012

A new perspective on Stein's so-called density approach is provided by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line and proposing a new Stein identity which is used to derive information inequalities in terms of the "generalized Fisher information distance".

### Use of exchangeable pairs in the analysis of simulations

- Mathematics
- 2004

The method of exchangeable pairs has emerged as an important tool in proving limit theorems for Poisson, normal and other classical approx- imations. Here the method is used in a simulation context.…

### Nourdin–Peccati analysis on Wiener and Wiener–Poisson space for general distributions

- Mathematics
- 2012

### An Introduction to Stein's Method

- Mathematics
- 2005

A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which…

### Normal Approximation by Stein's Method

- Mathematics
- 2010

Preface.- 1.Introduction.- 2.Fundamentals of Stein's Method.- 3.Berry-Esseen Bounds for Independent Random Variables.- 4.L^1 Bounds.- 5.L^1 by Bounded Couplings.- 6 L^1: Applications.- 7.Non-uniform…