Geodesic
Sharp bounds for expectations of spacings from decreasing density and failure rate families
Katarzyna Danielak1 ; Tomasz Rychlik2
1 Institute of Mathematics Polish Academy of Sciences P.O. Box 21 Śniadeckich 8 00-956 Warszawa, Poland
2 Institute of Mathematics Polish Academy of Sciences Chopina 12 87-100 Toruń, Poland
Applicationes Mathematicae, Tome 31 (2004) no. 4, pp. 369-395 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am31-4-1
Keywords: apply method projecting functions convex cones hilbert spaces derive sharp upper bounds expectations spacings samples coming restricted families distributions families considered distributions decreasing density decreasing failure rate characterize distributions which bounds attained

Katarzyna Danielak 1 ; Tomasz Rychlik 2

1 Institute of Mathematics Polish Academy of Sciences P.O. Box 21 Śniadeckich 8 00-956 Warszawa, Poland
2 Institute of Mathematics Polish Academy of Sciences Chopina 12 87-100 Toruń, Poland 
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 failure rate families},
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 failure rate families
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 from decreasing density and
 failure rate families
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Katarzyna Danielak; Tomasz Rychlik. Sharp bounds for expectations of spacings
 from decreasing density and
 failure rate families. Applicationes Mathematicae, Tome 31 (2004) no. 4, pp. 369-395. doi: 10.4064/am31-4-1

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