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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 5, Fasc. 2,
pages 221 - 224
 

LIMITING PROPERTIES OF DIFFERENCE BETWEEN THE SUCCESSIVE k -TH RECORD VALUES

Lesław Gajek

Abstract: Let (k) (Yn ) denote the sequence of the k -th record statistics corresponding to the sequence (Xi) of i.i.d. random variables. In this paper it is shown that (k) (k) k(Yn+1- Yn ) tends weakly (for k --> oo ) to the exponentially distributed random variable for a wide class of absolutely continuous random variables Xi.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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