Conditional limit results for type I polar distributions |
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Authors: | Enkelejd Hashorva |
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Affiliation: | (1) Department of Mathematical Statistics and Actuarial Science, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland |
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Abstract: | Let (S 1,S 2) = (R cos(Θ), R sin(Θ)) be a bivariate random vector with associated random radius R which has distribution function F being further independent of the random angle Θ. In this paper we investigate the asymptotic behaviour of the conditional survivor probability when u approaches the upper endpoint of F. On the density function of Θ 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 , which is then utilised to construct two estimators for the conditional distribution function . Furthermore, we allow Θ to depend on u. |
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Keywords: | Polar distributions Elliptical distributions Gumbel max-domain of attraction Conditional limit theorem Tail asymptotics Estimation of conditional distribution |
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