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On the density for sums of independent exponential, Erlang and gamma variates

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  • Edmond Levy

    (Stanmore)

Abstract

This paper re-examines the density for sums of independent exponential, Erlang and gamma random variables. By using a divided difference perspective, the paper provides a unified approach to finding closed-form formulae for such convolutions. In particular, the divided difference perspective for sums of Erlang variates suggests a new approach to finding the density for sums of independent gamma variates using fractional calculus.

Suggested Citation

  • Edmond Levy, 2022. "On the density for sums of independent exponential, Erlang and gamma variates," Statistical Papers, Springer, vol. 63(3), pages 693-721, June.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:3:d:10.1007_s00362-021-01256-x
    DOI: 10.1007/s00362-021-01256-x
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    References listed on IDEAS

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    1. Sim, C. H., 1992. "Point processes with correlated gamma interarrival times," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 135-141, September.
    2. Coelho, Carlos A., 1998. "The Generalized Integer Gamma Distribution--A Basis for Distributions in Multivariate Statistics," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 86-102, January.
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    Cited by:

    1. Suescún-Díaz, D. & Ibáñez-Paredes, M.C. & Chala-Casanova, J.A., 2023. "Stochastic radioactive decay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).

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