Abstract
This paper considers two classes of bivariate distributions having proportional (reversed) hazard rates models as their marginals. Various dependence properties of the proposed models are studied through their copulas.
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References
Clayton DG, Cuzick J (1985) Multivariate generalizations of the proportional hazards model. J R Stat Soc Ser A 148:82–117
Durante F (2009) Construction of non-exchangeable bivariate distribution functions. Stat Pap 50:383–391
Finkelstein MS (2003) On one class of bivariate distributions. Stat Probab Lett 65:1–6
Genest C, MacKey RJ (1986) Copules archimédiennes et familles de lois bidimensionnelles dont les marges sont données. Can J Stat 14:145–159
Genest C, Rivest L-P (2001) On the probability integral transformation. Stat Probab Lett 53:391–399
Gupta RC, Gupta PL, Gupta RD (1998) Modelling failure time data by Lehmman alternatives. Commun Stat Theory Methods 27:887–904
Gupta RD, Kundu D (2007) Generalized exponential distributions: Existing results and some recent developments. J Stat Plan Inference 137:3525–3536
Joe H (1997) Multivariate models and dependence concepts. Chapman & Hall, London
Klement EP, Mesiar R, Pap E (2005) Transformations of copulas. Kybernetika 41:425–434
Kundu D, Gupta RD (2010) A class of bivariate models with proportional reversed hazard marginals. Sankhy\(\bar{a}\) B 72:236–253
Marshall AW, Olkin I (1997) Adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84:641–652
Morillas PM (2005) A method to obtain new copulas from a given one. Metrika 61:169–184
Mudholkar GS, Huston AD (1996) The exponentiated Weibull family: some properties and a flood data application. Commun Stat Theory Methods 25:3059–3083
Nadarajah S (2006) The exponentiated type distributions. Acta Appl Math 92:97–111
Nassar MM, Eissa FH (2003) On the exponentiated Weibull distribution. Commun Stat Theory Methods 32:1317–1336
Nelsen RB (2006) An introduction to copulas, 2nd edn. Springer, New York
Pillai RN, Jayakumar K (1995) Discrete Mittag-Leffler distributions. Stat Probab Lett 23:271–274
Roy F (2002) Acharacterization of model approach for generating bivariate life distributions using reversed hazard rates. J Jpn Stat Soc 32:239–245
Sankaran PG, Gleeja VL (2006) On bivariate reversed hazard rates. J Jpn Stat Soc 36:213–224
Scarsini M (1984) On measures of concordance. Stochastica 8:201–218
Tibiletti L (1995) Quasi-concavity property of multivariate distribution functions. Ratio Mathematica 9: 27–36
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We acknowledge the helpful comments of two reviewers that led to several improvements in this paper.
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Dolati, A., Amini, M. & Mirhosseini, S.M. Dependence properties of bivariate distributions with proportional (reversed) hazards marginals. Metrika 77, 333–347 (2014). https://doi.org/10.1007/s00184-013-0440-1
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DOI: https://doi.org/10.1007/s00184-013-0440-1