Abstract
LetY k,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 valueY k,n has an increasing failure rate (IFR), thenY l,n (l<k) andY k+1,n+1(n≤k+1) also have IFR distributions. On the other hand, ifY k,n has a decreasing failure rate (DFR), thenY l,n (1>k) has also a DFR distribution. We also present some results concerning log convexity and log concavity ofY k,n .
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Raqab, M.Z., Amin, W.A. A note on reliability properties of k-record statistics. Metrika 46, 245–251 (1997). https://doi.org/10.1007/BF02717177
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DOI: https://doi.org/10.1007/BF02717177