A Note of Reliability Properties of K-Record Statistics

Let Y (formula) denote the nth (upper) k-record value of an infinite sequence of independent, identically distributed random variables with common continuous distribution function F. We show that if the nthk-record value Y (formula) has an increasing failure rate (IFR), then Y (formula) and Y (formula) also have IFR distributions. On the other hand, if Y (formula) has a decreasing failure rate (DFR), then Y (formula) has also a DFR distribution. We also present some results concerning log convexity and log concavity of Y (formula)