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Lattice polynomials of random variables

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  • Dukhovny, Alexander

Abstract

In many statistics and reliability theory models the object of interest is a random variable obtained from others by minimum and maximum operations. As a generalization, a random variable Y defined as a lattice polynomial of random arguments was introduced in Marichal [2006. Cumulative distribution function and moments of lattice polynomials. Statist. Probab. Lett. 76(12), 1273-1279] and studied in case of independent identically distributed arguments. Here, the cumulative distribution function of Y (in particular, order statistic) is studied for generally dependent arguments and special cases. A relation (presented in [Marichal, 2006. Cumulative distribution function and moments of lattice polynomials. Statist. Probab. Lett. 76(12), 1273-1279]) between Y and order statistics is proved to hold if and only if the arguments possess "cardinality symmetry".

Suggested Citation

  • Dukhovny, Alexander, 2007. "Lattice polynomials of random variables," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 989-994, June.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:10:p:989-994
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    1. Marichal, Jean-Luc, 2006. "Cumulative distribution functions and moments of lattice polynomials," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1273-1279, July.
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    Cited by:

    1. Marichal, Jean-Luc & Mathonet, Pierre & Waldhauser, Tamás, 2011. "On signature-based expressions of system reliability," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1410-1416, November.

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