Limit distributions for the ratio of the random sum of squares to the square of the random sum with applications to risk measures | Zendy

Sophie A. Ladoucette | Zendy; Jef Teugels | Zendy

Open Access

Limit distributions for the ratio of the random sum of squares to the square of the random sum with applications to risk measures

Author(s) -

Sophie A. Ladoucette,

Jef Teugels

Publication year - 2006

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim0694219l

Subject(s) - mathematics , independent and identically distributed random variables , combinatorics , limit (mathematics) , random variable , type (biology) , sequence (biology) , statistics , square (algebra) , distribution (mathematics) , discrete mathematics , mathematical analysis , geometry , ecology , genetics , biology

Let {X1,X2,...} be a sequence of independent and identically distributed positive random variables of Pareto-type and let {N (t); t 0} be a counting process independent of the Xi's. For any fixed t 0, define:

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