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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 25, Fasc. 2,
pages 197 - 210
 

BOUNDS ON THE BIAS OF APPROXIMATION OF FRACTIONAL RECORD VALUES

Mariusz Bieniek
Milena Bieniek
Dominik Szynal

Abstract: We present sharp bounds for an approximation of fractional k th record values by convex combinations of ordinary k th record values. The bounds are expressed in different scale units measured in p th central absolute moments of the underlying distribution. The distributions which attain the bounds are also specified. The bounds are derived by the projection method.

2000 AMS Mathematics Subject Classification: 62G30.

Key words and phrases: Fractional record values, projection method, Moriguti’s inequality, variation diminishing property.

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