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Random vectors with HNBUE-type marginal distributions

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  • Pellerey, Franco

Abstract

The problem of the preservation of non-parametric life distributions classes under addition of life lengths has been extensively studied in literature. In literature, however, independence among the random life lengths is often assumed. Here we show that for the HNBUE life distributions class (and for some other larger classes) this preservation property can be extended to non-independent summands, and, as a consequence, that convergence in law is equivalent to moment convergence within the family of random vectors with marginals in these classes. Related results, with an application in portfolio choice theory, are shown too.

Suggested Citation

  • Pellerey, Franco, 2000. "Random vectors with HNBUE-type marginal distributions," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 265-271, November.
    • Handle: RePEc:eee:stapro:v:50:y:2000:i:3:p:265-271
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    References listed on IDEAS

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    1. Hadar, Josef & Russell, William R., 1971. "Stochastic dominance and diversification," Journal of Economic Theory, Elsevier, vol. 3(3), pages 288-305, September.
    2. Masaaki Kijima & Masamitsu Ohnishi, 1996. "Portfolio Selection Problems Via The Bivariate Characterization Of Stochastic Dominance Relations1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 237-277, July.
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    Cited by:

    1. Li, Xiaohu & Lin, Jianhua, 2011. "Stochastic orders in time transformed exponential models with applications," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 47-52, July.
    2. F. Belzunce & J. Pinar & J. Ruiz, 2005. "On testing the dilation order and HNBUE alternatives," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(4), pages 803-815, December.
    3. Pavlova, Kristina P. & Cai, Jun & Willmot, Gordon E., 2006. "The preservation of classes of discrete distributions under convolution and mixing," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 391-405, April.
    4. Mulero, Julio & Pellerey, Franco & Rodríguez-Griñolo, Rosario, 2010. "Stochastic comparisons for time transformed exponential models," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 328-333, April.

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