  The paper concerns the optimal upper bounds on the expectations of the kth
record values (k >= 1) centered about the sample mean. We consider the case,
when the records are based on the infinite sequence of the independent
identically distributed random variables, which distribution function is
restricted to the family of distributions with the increasing generalized
failure rate (IGFR). Such a class can be defined in terms of the convex orders
of some distribution functions. Particularly important examples of IGFR class
are the distributions with the increasing density (ID) and increasing failure
rate (IFR). Presented bounds were obtained with use of the projection method,
and are expressed in the scale units based on the standard deviation of the
underlying distribution function.
