Reconstruction of previous failure times and records

For the sequences of independent identically distributed random variables with continuous distributions, we provide the optimal upper bounds for the increments of order and record statistics under condition that the values of future order statistics and records are known. The bounds are expressed in terms of quantiles and absolute moments centered about the quantiles of the parent distribution. We also describe the distributions which approach the bounds with arbitrary desired accuracy.The second author was supported by the Polish State Committee for Scientific Research (KBN) under Grant 5 P03A 012 20Received November 2003