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 th record values by
convex combinations of ordinary th record values. The bounds are expressed in different
scale units measured in 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.