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On construction of general classes of bivariate distributions

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  • Lee, Hyunju
  • Cha, Ji Hwan

Abstract

In this study, taking into account the physics of failure (death) and the interrelationship between the items involved, we propose a general methodology for constructing new ‘classes of bivariate distributions’. The approach is based on the stochastic modeling of the residual lifetime of an item after the failure of the other item. We derive the joint and the corresponding marginal distributions in a class constructed from the modeling of conditional failure rate. It is shown that the proposed new class includes several well-known bivariate distributions as special bivariate models. As illustrated, a number of new families of bivariate distributions are generated from the new class proposed in this paper. Furthermore, we briefly discuss the relationship to Freund’s bivariate exponential distribution.

Suggested Citation

  • Lee, Hyunju & Cha, Ji Hwan, 2014. "On construction of general classes of bivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 151-159.
    • Handle: RePEc:eee:jmvana:v:127:y:2014:i:c:p:151-159
    DOI: 10.1016/j.jmva.2014.02.007
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    References listed on IDEAS

    as
    1. Ji Hwan Cha & Jie Mi, 2011. "On a Stochastic Survival Model for a System Under Randomly Variable Environment," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 549-561, September.
    2. Sarhan, Ammar M. & Balakrishnan, N., 2007. "A new class of bivariate distributions and its mixture," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1508-1527, August.
    3. Maxim Finkelstein & Ji Hwan Cha, 2013. "Burn-in for Heterogeneous Populations," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 261-312, Springer.
    4. Paul H. Kvam & Edsel A. Pena, 2005. "Estimating Load-Sharing Properties in a Dynamic Reliability System," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 262-272, March.
    5. Lee, Larry, 1979. "Multivariate distributions having Weibull properties," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 267-277, June.
    6. Maxim Finkelstein & Ji Hwan Cha, 2013. "Shocks as Burn-in," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 313-361, Springer.
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    Cited by:

    1. Lee, Hyunju & Cha, Ji Hwan, 2015. "Construction of two new general classes of bivariate distributions based on stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 75-85.
    2. Hyunju Lee & Ji Hwan Cha, 2020. "A new general class of discrete bivariate distributions constructed by using the likelihood ratio," Statistical Papers, Springer, vol. 61(3), pages 923-944, June.
    3. Debasis Kundu, 2020. "On a General Class of Discrete Bivariate Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 270-304, November.
    4. Na Young Yoo & Ji Hwan Cha, 2024. "General classes of bivariate distributions for modeling data with common observations," Statistical Papers, Springer, vol. 65(8), pages 5219-5238, October.

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