nach oben

Erschienen in:

2015 | OriginalPaper | Buchkapitel

6. Extended Marshall–Olkin Model and Its Dual Version

verfasst von : Jayme Pinto, Nikolai Kolev

Erschienen in: Marshall ̶ Olkin Distributions - Advances in Theory and Applications

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

We propose an extension of the generalized bivariate Marshall–Olkin model assuming dependence between the random variables involved. Probabilistic, aging properties, and survival copula representation of the extended model are obtained and illustrated by examples. Bayesian analysis is performed and possible applications are discussed. A dual version of extended Marshall–Olkin model is introduced and related stochastic order comparisons are presented.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Marshall–Olkin Machinery and Power Mixing: The Mixed Generalized Marshall–Olkin Distribution

Baglioni, A., Cherubini, U.: Within and between systemic country risk. Theory and evidence from the sovereign crisis in Europe. J. Econ. Dyn. Control 37, 1581–1597 (2013)CrossRefMathSciNet

Balakrishnan, N., Lai, C.-D.: Continuous Bivariate Distributions, 2nd edn. Springer, New York (2009)MATH

Barlow, R., Proschan, F.: Statistical Theory of Reliability and Life Testing. Silver Spring, Maryland (1981)

Barlow, R., Marshall, A., Proschan, F.: Properties of probability distributions with monotone hazard rate. Ann. Math. Stat. 34, 375–389 (1963)CrossRefMATHMathSciNet

Bassan, B., Spizzichino, F.: Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes. J. Multivar. Anal. 93, 313–339 (2005)CrossRefMATHMathSciNet

Block, H., Basu, A.: A continuous bivariate exponential extension. J. Am. Stat. Assoc. 69, 1031–1037 (1974)MATHMathSciNet

Dabrowska, D.: Kaplan-Meier estimate on the plane. Ann. Stat. 16, 1475–1489 (1988)CrossRefMATHMathSciNet

Dimitrov, B., Kolev, N.: The BALM copula. Int. J. Stoch. Anal. 2013, 1–6 (2013)CrossRefMathSciNet

Fang, R., Li, X.: A note on bivariate dual generalized Marshall-Olkin distributions with applications. Probab. Eng. Inf. Sci. 27, 367–374 (2013)CrossRefMATHMathSciNet

10.

Freund, J.: A bivariate extension of the exponential distribution. J. Am. Stat. Assoc. 56, 971–977 (1961)CrossRefMATHMathSciNet

11.

Gumbel, E.: Bivariate exponential distributions. J. Am. Stat. Assoc. 55, 698–707 (1960)CrossRefMATHMathSciNet

12.

Gupta, R.C., Gupta, R.D., Gupta, P.L.: Modeling failure time data by Lehman alternatives. Commun. Stat. Theory Methods 27, 887–904 (1988)CrossRef

13.

Jaschke, S., Siburg, K., Stoimenov, P.: Modelling dependence of extreme events in energy markets using tail copulas. J. Energy Mark. 5(4), 63–80 (2013)

14.

Karlis, D.: ML estimation for multivariate shock models via an EM algorithm. Ann. Inst. Stat. Math. 55, 817–830 (2003)CrossRefMATHMathSciNet

15.

Keilson, J., Sumita, U.: Uniform stochastic ordering and related inequalities. Can. J. Stat. 10, 181–198 (1982)CrossRefMATHMathSciNet

16.

Kundu, D., Dey, A.: Estimating the parameters of the Marshall-Olkin bivariate Weibull distribution by EM algorithm. Comput. Stat. Data Anal. 53, 956–965 (2009)CrossRefMATHMathSciNet

17.

Kundu, D., Gupta, R.: Modified Sarhan-Balakrishnan singular bivariate distribution. J. Stat. Plan. Inference 140, 525–538 (2010)MathSciNet

18.

Kundu, D., Gupta, A.: Bayes estimation for the Marshall-Olkin bivariate Weibull distribution. Comput. Stat. Data Anal. 57, 271–281 (2013)CrossRefMathSciNet

19.

Lehmann, E.: Some concepts of dependence. Ann. Math. Stat. 37, 1137–1153 (1966)CrossRefMATH

20.

Li, X.: Duality of the multivariate distributions of Marshall-Olkin type and tail dependence. Commun. Stat. Theory Methods 37, 1721–1733 (2008)CrossRefMATH

21.

Li, X., Pellerey, F.: Generalized Marshall-Olkin distributions and related bivariate aging properties. J. Multivar. Anal. 102, 1399–1409 (2011)CrossRefMATHMathSciNet

22.

Lunn, D., Spiegelhalter, D., Thomas, A., Best, N.: The BUGS project: evolution, critique and future directions (with discussion). Stat. Med. 28, 3049–3082 (2009)CrossRefMathSciNet

23.

Mai, J.-F., Scherer, M.: Simulating Copulas. Imperial College Press, London (2012)CrossRefMATH

24.

Marshall, A., Olkin, I.: A multivariate exponential distribution. J. Am. Stat. Assoc. 62, 30–41 (1967)CrossRefMATHMathSciNet

25.

McNeil, A., Frey, L., Embrechts, P.: Quantitative Risk Management. Princeton University Press, Princeton (2005)MATH

26.

Meintanis, S.: Test of fit for Marshall-Olkin distributions with applications. J. Stat. Plan. Inference 137, 3954–3963 (2007)CrossRefMATHMathSciNet

27.

Mirhosseini, S., Amini, M., Kundu, D., Dolati, A.: On a new absolutely continuous bivariate generalized exponential distribution. To appear in Statistical Methods and Applications (2015)

28.

Mohsin, M., Kazianka, H., Pilz, J., Gebhardt, A.: A new bivariate exponential distribution for modeling moderately negative dependence. Stat. Methods Appl. 23, 123–148 (2014)CrossRefMathSciNet

29.

Mulero, J., Pellerey, F.: Bivariate aging properties under Archimedean dependence structures. Commun. Stat. Theory Methods 39, 3108–3121 (2010)CrossRefMATHMathSciNet

30.

Muliere, P., Scarsini, M.: Generalization of Marshall-Olkin type of distributions. Ann. Inst. Stat. Math. 39, 429–441 (1987)CrossRefMATHMathSciNet

31.

Nelsen, R.: An Introduction to Copulas, 2nd edn. Springer, New York (2006)MATH

32.

Pinto, J.: Deepening the notions of dependence and aging in bivariate probability distributions. Ph.D. thesis, Sao Paulo University (2014)

33.

Pinto, J., Kolev, N.: Sibuya-type bivariate lack of memory property. J. Multivar. Anal. 134, 119–128 (2015)CrossRefMATHMathSciNet

34.

Pinto, J., Kolev, N.: Copula representations for invariant dependence functions. In: Glau, K., Scherer, M., Zagst, R. (eds.) Innovations in Quantitative Risk Management. Springer Series in Probability & Statistics, vol. 99, pp. 411–421. Springer, New York (2015)CrossRef

35.

Sankaran, P.G., Gleeja, V.L.: On bivariate reversed hazard rates. J. Jpn. Stat. Soc. 36, 213–224 (2006)CrossRefMATHMathSciNet

36.

Shaked, M., Shanthikumar, J.: Stochastic Orders. Springer, New York (2007)CrossRefMATH

37.

Shoaee, S., Khorram, E.: A new absolute continuous bivariate generalized exponential distribution. J. Stat. Plan. Inference 142, 2203–2220 (2012)CrossRefMATHMathSciNet

38.

Sibuya, M.: Bivariate extreme statistics I. Ann. Inst. Stat. Math. 11, 195–210 (1960)CrossRefMATHMathSciNet

39.

Singpurwalla, N.: Reliability Analysis: A Bayesian Perspective. Wiley, Chichester (2006)

40.

Spiegelhalter, D., Best, N., Carlin, B., van der Linde, A.: Bayesian measures of model complexity and fit (with discussion). J. R. Stat. Soc. Ser. A 64, 583–639 (2002)CrossRefMATH

41.

Spiegelhalter, D., Thomas, A., Best, N., Lunn, D.: WinBugs Version 1.4, User Manual. Institute of Public Health and Department of Epidemiology and Public Health. Imperial College School of Medicine, London (2003)

Titel: Extended Marshall–Olkin Model and Its Dual Version
verfasst von: Jayme Pinto
Nikolai Kolev
Verlag: Springer International Publishing
Buch: Marshall ̶ Olkin Distributions - Advances in Theory and Applications
Print ISBN: 978-3-319-19038-9

Electronic ISBN: 978-3-319-19039-6

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-319-19039-6_6

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"