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Sharp bounds on the expectations of linear combinations of kth records expressed in the Gini mean difference units

100%

Kozyra P. M. , Rychlik T.

2018

tom Vol. 38, Fasc. 1

39--59

We describe a method of calculating sharp lower and upper bounds on the expectations of linear combinations of kth records Expressem 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 kth records and their differences. We also present the families of distributions which attain the bounds in the limit.

Evaluating improvements of records

63%

Rychlik T.

Applicationes Mathematicae

1996-1997

tom 24

nr 3

315-324

We evaluate the extreme differences between the consecutive expected record values appearing in an arbitrary i.i.d. sample in the standard deviation units. We also discuss the relevant estimates for parent distributions coming from restricted families and other scale units.