Some tests against aging based on the total time on test transform
1980 (English)Report (Other academic)
Let F be a life distribution with survival function F = 1 - F and00 —finite mean y * j n F(x)dx. The scaled total time on test transform-1F( t ) —<P,,(t) = /n /F(x)dx/y was introduced by Barlow and Campo (1975) as ar Utool in the statistical analysis of life data. The properties IFR, IFRA, NBUE, DMRL and heavy-tailedness can be translated to properties of tp„(t).rWe discuss the previously known of these relationships and present some new results. Guided by properties of <P„(t) we suggest some test statisticsrfor testing exponentiality against IFR, IFRA, NBUE, DMRL and heavy-tailed-ness, respectively. The asymptotic distributions of the statistics are derived and the asymptotic efficiencies of the tests are studied. The power for some of the tests is estimated by simulation for some alternatives when the sample size is n = 10 or n = 20.
Place, publisher, year, edition, pages
Umeå: Umeå universitet , 1980. , 40 p.
, Statistical research report, ISSN 0348-0399 ; 1979:4
Life distribution, survival function, aging, exponential distribution, IFR, IFRA, NBUE, DMRL, hypothesis testing, efficiency, consistency, power
IdentifiersURN: urn:nbn:se:umu:diva-78993OAI: oai:DiVA.org:umu-78993DiVA: diva2:638395
This is a revised version of Statistical Research Report 1979-4, Department of Mathematical Statistics, University of Umeå.
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