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The Bivariate Exponential Distribution; A Review And Some New Results

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  • V. Barnett

Abstract

Various models have been proposed as bivariate forms of the exponential distribution. A brief but comprehensive review is presented which classifies, interrelates and contrasts the different models and outlines what is known about distributional properties, applicability and estimation and testing of parameters (particularly the association parameter). Some new results are presented for one particular model. Maximum likelihood, and moment–type, estimators of the association parameter are examined. Asymptotic variances are derived and attention is given to the relative efficiency of the estimators and to problems of their evaluation.

Suggested Citation

  • V. Barnett, 1985. "The Bivariate Exponential Distribution; A Review And Some New Results," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 39(4), pages 343-356, December.
    • Handle: RePEc:bla:stanee:v:39:y:1985:i:4:p:343-356
    DOI: 10.1111/j.1467-9574.1985.tb01153.x
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    Cited by:

    1. Yusuf Can Sevil & Tugba Ozkal Yildiz, 2022. "Gumbel’s bivariate exponential distribution: estimation of the association parameter using ranked set sampling," Computational Statistics, Springer, vol. 37(4), pages 1695-1726, September.
    2. Kim, Bara & Kim, Jeongsim, 2011. "Representation of Downton’s bivariate exponential random vector and its applications," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1743-1750.
    3. Nadarajah Saralees & Kotz Samuel, 2006. "Determination of Software Reliability based on Multivariate Exponential, Lomax and Weibull Models," Monte Carlo Methods and Applications, De Gruyter, vol. 12(5), pages 447-459, November.
    4. Samuel Kotz & J. Renevan Dorp, 2002. "A versatile bivariate distribution on a bounded domain: Another look at the product moment correlation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(8), pages 1165-1179.
    5. Agustín Hernández-Bastida & M. Fernández-Sánchez, 2012. "A Sarmanov family with beta and gamma marginal distributions: an application to the Bayes premium in a collective risk model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(4), pages 391-409, November.
    6. Regoli, Giuliana, 2009. "A class of bivariate exponential distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1261-1269, July.

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