Some properties of the HNBUE and HNWUE classes of life distributions
1980 (English)Report (Other academic)
The HNBUE (HNWUE) class of life distributions (i.e. for which f F (x)dx< (>)00 t< (>) y exp(-t/y) for t > 0, where y = / F(x)dx) is studied. We prove0that the HNBUE (HNWUE) class is larger than the NBUE (NWUE) class. We alsopresent some characterizations of the HNBUE (HNWUE) property by using theTotal Time on Test (TTT-) transform and the Laplace transform. Further weexamine whether the HNBUE (HNWUE) property is preserved under the reliabilityoperations (1) formation of coherent structure, (2) convolution and(3) mixture. Some bounds on the moments and on the survival function of aHNBUE (HNWUE) life distribution are also presented. The class of distributionswith the discrete HNBUE (discrete HNWUE) property (i.e. for which00 00 00I P. < (>) y(l-l/y)k for k = 0,1,2j=k J "where yi=0 JI p. and P. = E p, )J k=j+l kis also studied.
Place, publisher, year, edition, pages
Umeå: Umeå universitet , 1980. , 48 p.
, Statistical research report, ISSN 0348-0399 ; 1980:8
Life distribution, survival function, survival probability, HNBUE, HNWUE, discrete HNBUE, discrete HNWUE, TTT-transform, Laplace transform, damage model, coherent structure, convolution, mixture
IdentifiersURN: urn:nbn:se:umu:diva-78994OAI: oai:DiVA.org:umu-78994DiVA: diva2:638402
There are some occurring misspellings in the formulas in the abstract on this webpage. Read the abstract in the full-text document for correct spelling in formulas, see the downloadable file.2013-07-302013-07-302013-07-30Bibliographically approved