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Bounds on the bias of approximation of fractional record values

Bieniek M., Bieniek M., Szynal D.

Probability and Mathematical Statistics

2005

Vol. 25, Fasc. 2

197--210

We present sharp bounds for an approximation of fractional kth record values by convex combinations of ordinary kth record values. The bounds are ex-pressed in different scale units measured in pth central absolute moments of the under-lying distribution. The distributions which attain the bounds are also specified. The bounds are derived by the projection method.

Tsallis' entropy bounds for generalized order statistics

Kałuszka M., Okolewski A.

Probability and Mathematical Statistics

2004

Vol. 24, Fasc. 2

253--262

We present sharp bounds for expectations of generalized order statistics with random indices expressed in terms of Tsallis’ entropy. The bounds are attainable and provide new characterizations of some nontrivial distributions. No restrictions are imposed on the parameters of the generalized order statistics model.