Sharp bounds for expectations of spacings from decreasing density and failure rate families

Volume 31 / 2004

Katarzyna Danielak, Tomasz Rychlik Applicationes Mathematicae 31 (2004), 369-395 MSC: Primary 60E15, 62G30; Secondary 62N05. DOI: 10.4064/am31-4-1


We apply the method of projecting functions onto convex cones in Hilbert spaces to derive sharp upper bounds for the expectations of spacings from i.i.d. samples coming from restricted families of distributions. Two families are considered: distributions with decreasing density and with decreasing failure rate. We also characterize the distributions for which the bounds are attained.


  • Katarzyna DanielakInstitute of Mathematics
    Polish Academy of Sciences
    P.O. Box 21
    Śniadeckich 8
    00-956 Warszawa, Poland
  • Tomasz RychlikInstitute of Mathematics
    Polish Academy of Sciences
    Chopina 12
    87-100 Toruń, Poland

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