# Conditional limit results for type I polar distributions

### Details

Serval ID

serval:BIB_7CF61A6B183E

Type

**Article**: article from journal or magazin.

Collection

Publications

Fund

Title

Conditional limit results for type I polar distributions

Journal

Extremes

ISSN

1386-1999

1572-915X ([electronic])

1572-915X ([electronic])

Publication state

Published

Issued date

2009

Peer-reviewed

Oui

Volume

12

Number

3

Pages

239-263

Language

english

Abstract

Let (S(1), S(2)) = ( R cos(Theta), R sin(Theta)) be a bivariate random vector with associated random radius R which has distribution function F being further independent of the random angle similar to In this paper we investigate the asymptotic behaviour of the conditional survivor probability (I) over bar rho, u( y) := P {rho S(1) + root 1 - rho(2)S(2) > y|S(1) > u}, rho is an element of (- 1, 1), is an element of IR when u approaches the upper endpoint of F. On the density function of similar to we impose a certain local asymptotic behaviour at 0, whereas for F we require that it belongs to the Gumbel max-domain of attraction. The main result of this contribution is an asymptotic expansion of I., u, which is then utilised to construct two estimators for the conditional distribution function 1 - (I) over bar rho,u. Furthermore, we allow Theta to depend on u.

Keywords

Polar distributions, Elliptical distributions, Gumbel max-domain of attraction, Conditional limit theorem, Tail asymptotics, Estimation of conditional distribution

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Create date

03/09/2010 10:17

Last modification date

03/03/2018 17:38