Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
On some classes of bivariate life distributions
Umeå University, Faculty of Science and Technology, Mathematical statistics.
1980 (English)Report (Other academic)
Abstract [en]

During the last years efforts have been made in order to define suitable bivariate and multivariate extensions of the univariate IFR, IFRA, NBU NBUE and DMRL classes (with duals) of life distributions. In this paper we suggest two new bivariate NBUE (NWUE) and several bivariate HNBUE (HNWUE) definitions. Furthermore, we discuss some of the classes of multivariate life distributions proposed by Buchanan and Singpurwalla (1977). We also study two bivariate shock models. Suppose that two devices are subjected to shocks of some kind. Let P(k^,k2), k^,k2 = 0,1,2,..., denote the probability that the devices survive k^ and k2 shocks, respectively, and let T. denote the time to failure of device number j, j = 1,2, and let H(t^,t2) = P(T^ > t^,T2 > t2)• We study the shock models by Marshall and Olkin and by Buchanan and Singpurwalla and give sufficient conditions, containing P(k^,k2), k^,k2 = 0,1,2,..., under which H.(t^,t2) is bivariate NBU (NWU), bivariate NBUE (NWUE) and bivariate HNBUE (HNWUE) of different forms.

Place, publisher, year, edition, pages
Umeå: Umeå universitet , 1980. , 50 p.
Series
Statistical research report, ISSN 0348-0399 ; 1980:9
Keyword [en]
Life distribution, survival function, bivariate exponential distribution, bivariate geometric distribution, bivariate NBU, bivariate NBUE, bivariate HNBUE, bivariate shock models
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-78996OAI: oai:DiVA.org:umu-78996DiVA: diva2:638423
Projects
digitalisering@umu
Note

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.

Available from: 2013-07-30 Created: 2013-07-30 Last updated: 2013-07-30Bibliographically approved
In thesis
1. Properties and tests for some classes of life distributions
Open this publication in new window or tab >>Properties and tests for some classes of life distributions
1980 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

A life distribution and its survival function F = 1 - F with finitemean y = /q F(x)dx are said to be HNBUE (HNWUE) if F(x)dx < (>)U exp(-t/y) for t > 0. The major part of this thesis deals with the classof HNBUE (HNWUE) life distributions. We give different characterizationsof the HNBUE (HNWUE) property and present bounds on the moments and on thesurvival function F when this is HNBUE (HNWUE). We examine whether theHNBUE (HNWUE) property is preserved under some reliability operations andstudy some test statistics for testing exponentiality against the HNBUE(HNWUE) property.The HNBUE (HNWUE) property is studied in connection with shock models.Suppose that a device is subjected to shocks governed by a counting processN = {N(t): t > 0}. The probability that the device survives beyond t isthen00H(t) = S P(N(t)=k)P, ,k=0where P^ is the probability of surviving k shocks. We prove that His HNBUE (HNWUE) under different conditions on N and * ^orinstance we study the situation when the interarrivai times between shocksare independent and HNBUE (HNWUE).We also study the Pure Birth Shock Model, introduced by A-Hameed andProschan (1975), and prove that H is IFRA and DMRL under conditions whichdiffer from those used by A-Hameed and Proschan.Further we discuss relationships between the total time on test transformHp^(t) = /q ^F(s)ds , where F \t) = inf { x: F(x) > t}, and differentclasses of life distributions based on notions of aging. Guided by propertiesof we suggest test statistics for testing exponentiality agains t IFR,IFRA, NBUE, DMRL and heavy-tailedness. Different properties of these statisticsare studied.Finally, we discuss some bivariate extensions of the univariate properties NBU, NBUE, DMRL and HNBUE and study some of these in connection with bivariate shock models.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 1980. 16 p.
Keyword
Life distribution, survival function, exponential distribution, IFR, IFRA, NBUE, DMRL, HNBUE, shock model, total time on test transform, testing of exponentiality
National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-78990 (URN)
Public defence
1980-10-17, Samhällsvetarhuset, hörsal D, Umeå universitet, Umeå, 09:15
Projects
digitalisering@umu
Note

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.

Available from: 2013-07-30 Created: 2013-07-30 Last updated: 2013-07-30Bibliographically approved

Open Access in DiVA

On some classes of bivariate life distributions(2802 kB)142 downloads
File information
File name FULLTEXT02.pdfFile size 2802 kBChecksum SHA-512
1541aeaca548f3df535e11a31fb5e43bafce20fe7f73116cde6a03d2437ac6e173e84ac16ca08c503dd073cf06103bc92d503ccb907c98476a2ad3a5e68a3ad1
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Klefsjö, Bengt
By organisation
Mathematical statistics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 142 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 67 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf