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The Bivariate Lack-of-Memory Distributions

Author

Listed:
  • Gwo Dong Lin

    (Academia Sinica)

  • Xiaoling Dou

    (Waseda University)

  • Satoshi Kuriki

    (The Institute of Statistical Mathematics)

Abstract

We treat all the bivariate lack-of-memory (BLM) distributions in a unified approach and develop some new general properties of the BLM distributions, including joint moment generating function, product moments, and dependence structure. Necessary and sufficient conditions for the survival functions of BLM distributions to be totally positive of order two are given. Some previous results about specific BLM distributions are improved. In particular, we show that both the Marshall–Olkin survival copula and survival function are totally positive of all orders, regardless of parameters. Besides, we point out that Slepian’s inequality also holds true for BLM distributions.

Suggested Citation

  • Gwo Dong Lin & Xiaoling Dou & Satoshi Kuriki, 2019. "The Bivariate Lack-of-Memory Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 273-297, December.
    • Handle: RePEc:spr:sankha:v:81:y:2019:i:2:d:10.1007_s13171-017-0119-1
    DOI: 10.1007/s13171-017-0119-1
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    References listed on IDEAS

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    1. Jones, M. C., 1998. "Constant Local Dependence," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 148-155, February.
    2. Li, Xiaohu & Pellerey, Franco, 2011. "Generalized Marshall-Olkin distributions and related bivariate aging properties," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1399-1409, November.
    3. H. Kulkarni, 2006. "Characterizations and Modelling of Multivariate Lack of Memory Property," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(2), pages 167-180, October.
    4. Bassan, Bruno & Spizzichino, Fabio, 2005. "Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 313-339, April.
    5. Marshall, Albert W. & Olkin, Ingram, 2015. "A bivariate Gompertz–Makeham life distribution," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 219-226.
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