Publication Cover
Statistics
A Journal of Theoretical and Applied Statistics
Volume 40, 2006 - Issue 5
126
Views
9
CrossRef citations to date
0
Altmetric
Original Articles

Log-concavity of the extremes from Gumbel bivariate exponential distributions

&
Pages 415-433 | Received 24 May 2005, Published online: 01 Feb 2007

References

  • Dhaene , J. and Goovaerts , M. J. 1997 . On the dependency of risks in the individual life model . Insurance: Mathematics and Economics , 19 : 243 – 253 .
  • Ambagaspitiya , R. S. 1999 . On the distributions of two classes of correlated aggregate claims . Insurance: Mathematics and Economics , 24 : 301 – 308 .
  • Denuit , M. , Genest , C. and Marceau , E. 1999 . Stochastic bounds on sum of dependent risks . Insurance: Mathematics and Economics , 25 : 85 – 104 .
  • Albrecher , H. and Teugels , J. L. 2004 . Exponential behavior in the presence of dependence in risk theory . EURANDOM Research Report 2004–011
  • Cai , J. and Li , H. 2005 . Multivariate risk model of phase type . Insurance: Mathematics and Economics , 36 : 137 – 152 .
  • Blackorby , C. and Schworm , W. 1984 . The structure of economies with aggregate measures of capital: a complete characterization . Review of Economic Studies , 51 : 633 – 650 .
  • Miravete , E. J. 1996 . Screening consumers through alternative pricing mechanisms . Journal of Regulatory Economics , 9 : 111 – 132 .
  • Baron , D. P. and Besanko , D. 1999 . Informational alliances . Review of Economic Studies , 66 : 743 – 768 .
  • Biais , B. , Martimort , D. and Rochet , J. C. 2000 . Competing mechanisms in a common value environment . Econometrica , 68 : 799 – 837 .
  • Chan , W. S. , Yang , H. and Zhang , L. 2003 . Some results on ruin probabilities in a two-dimensional risk model . Insurance: Mathematics and Economics , 32 : 345 – 358 .
  • Milgrom , P. R. and Weber , R. J. 1982 . A theory of auctions and competitive bidding . Econometrica , 50 : 1089 – 1122 .
  • An , M. Y. 1998 . Logconcavity versus logconvexity: a complete characterization . Journal of Economic Theory , 80 : 350 – 369 .
  • Miravete , E. J. 2002 . Preserving log-concavity under convolution: comment . Econometrica , 70 : 1253 – 1254 .
  • Bagnoli , M. and Bergstrom , T. 2005 . Log-concave probability and its applications . Economic Theory , 26 : 445 – 469 .
  • Baggs , G. E. and Nagaraja , H. N. 1996 . Reliability properties of order statistics from bivariate exponential distributions . Communications in Statistics—Stochastic Models , 12 : 611 – 631 .
  • Gupta , P. L. and Gupta , R. C. 1997 . On the multivariate normal hazard . Journal of Multivariate Analysis , 62 : 64 – 73 .
  • Gupta , P. L. and Gupta , R. C. 2001 . Failure rate of the minimum and maximum of a multivariate normal distribution . Metrika , 53 : 39 – 49 .
  • Ma , C. 2000 . A note on the multivariate normal hazard . Journal of Multivariate Analysis , 73 : 282 – 283 .
  • Franco , M. and Vivo , J. M. 2002 . Reliability properties of series and parallel systems from bivariate exponential models . Communications in Statistics—Theory and Methods , 31 : 2349 – 2360 .
  • Gupta , R. C. 2005 . Reliability functions of bivariate distributions with second kind of beta conditionals . Statistics , 39 : 43 – 52 .
  • Gumbel , E. J. 1960 . Bivariate exponential distributions . Journal of the American Statistical Association , 55 : 698 – 707 .
  • Yaari , M. 1987 . The dual theory of choice under risk . Econometrica , 55 : 95 – 115 .
  • Hutchison , T. P. and Lai , C. D. 1990 . Continuous Bivariate Distributions, Emphasizing Applications , Australia : Rumsby Scientific Publishing .
  • Kotz , S. , Balakrishnan , N. and Johnson , N. L. 2000 . Continuous Multivariate Distributions , New York : Wiley .
  • Steutel , F. W. 1967 . Note on the infinite divisibility of exponential mixtures . The Annals of Mathematical Statistics , 38 : 1303 – 1305 .
  • Harris , C. M. , Marchal , W. G. and Botta , R. F. 1992 . A note on generalized hyperexponential distributions . Communications in Statistics—Theory and Methods , 8 : 179 – 191 .
  • Bartholomew , D. J. 1969 . Sufficient conditions for a mixture of exponentials to be a probability density function . The Annals of Mathematical Statistics , 40 : 2183 – 2188 .
  • Barlow , R. E. and Proschan , F. 1975 . Statistical Theory Of Reliability And Life Testing: Probability Models , New York : Holt, Rinehart and Winston .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.