Displaying similar documents to “Sharp bounds for expectations of spacings from decreasing density and failure rate families”

Optimal mean-variance bounds on order statistics from families determined by star ordering

Tomasz Rychlik (2002)

Applicationes Mathematicae

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We present optimal upper bounds for expectations of order statistics from i.i.d. samples with a common distribution function belonging to the restricted family of probability measures that either precede or follow a given one in the star ordering. The bounds for families with monotone failure density and rate on the average are specified. The results are obtained by projecting functions onto convex cones of Hilbert spaces.

Evaluating improvements of records

Tomasz Rychlik (1997)

Applicationes Mathematicae

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We evaluate the extreme differences between the consecutive expected record values appearing in an arbitrary i.i.d. sample in the standard deviation units. We also discuss the relevant estimates for parent distributions coming from restricted families and other scale units.

Discrete Lundberg-type bounds with actuarial applications

Kristina Sendova (2007)

ESAIM: Probability and Statistics

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Different kinds of renewal equations repeatedly arise in connection with renewal risk models and variations. It is often appropriate to utilize bounds instead of the general solution to the renewal equation due to the inherent complexity. For this reason, as a first approach to construction of bounds we employ a general Lundberg-type methodology. Second, we focus specifically on exponential bounds which have the advantageous feature of being closely connected to the asymptotic behavior...