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A generalization of the Eulerian numbers with a probabilistic application

Author

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  • Harris, Bernard
  • Park, C. J.

Abstract

In this paper we study a generalization of the Eulerian numbers and a class of polynomials related to them. An interesting application to probability theory is given in Section 3. There we use these extended Eulerian numbers to construct an uncountably infinite family of lattice random variables whose first n moments coincide with the first n moments of the sum of n+1 uniform random variables. A number of combinatorial identities are also deduced.

Suggested Citation

  • Harris, Bernard & Park, C. J., 1994. "A generalization of the Eulerian numbers with a probabilistic application," Statistics & Probability Letters, Elsevier, vol. 20(1), pages 37-47, May.
    • Handle: RePEc:eee:stapro:v:20:y:1994:i:1:p:37-47
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    Cited by:

    1. Fu, James C. & Lou, W. Y. Wendy & Wang, Yueh-Jir, 1999. "On the exact distributions of Eulerian and Simon Newcomb numbers associated with random permutations," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 115-125, April.
    2. James C. Fu & Wan-Chen Lee & Hsing-Ming Chang, 2023. "On Distribution of the Number of Peaks and the Euler Numbers of Permutations," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-13, June.
    3. James C. Fu, 2012. "On the Distribution of the Number of Occurrences of an Order-Preserving Pattern of Length Three in a Random Permutation," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 831-842, September.

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