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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 38, Fasc. 3,
pages 39 - 59
DOI: 10.19195/0208-4147.38.1.3
 

SHARP BOUNDS ON THE EXPECTATIONS OF LINEAR COMBINATIONS OF kth RECORDS EXPRESSED IN THE GINI MEAN DIFFERENCE UNITS

Paweł Marcin Kozyra
Tomasz Rychlik

Abstract: We describe a method of calculating sharp lower and upper bounds on the expectations of linear combinations of k th records expressed in the Gini mean difference units of the original i.i.d. observations. In particular, we provide sharp lower and upper bounds on the expectations of k th records and their differences. We also present the families of distributions which attain the bounds in the limit.

2010 AMS Mathematics Subject Classification: Primary: 60E15, 62G32.

Keywords and phrases: Expectation, Gini mean difference, sharp bound, k th record.

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