Let Yk,n 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 nth k-record value Yk,n has an increasing failure rate (IFR), then Yl,n(l < k) and Yk+1,n+1(n ≤ k + 1) also have IFR distributions. On the other hand, if Yk,n has a decreasing failure rate (DFR), then Yl,n(1 > k) has also a DFR distribution. We also present some results concerning log convexity and log concavity of Yk,n.
