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2 results

  • A geometric interpretation of the relations between the exponential and generalized Erlang distributions

  • Michel Dehon, Guy Latouche
  • Journal:
    Advances in Applied Probability / Volume 14 / Issue 4 / December 1982
    Published online by Cambridge University Press:
    01 July 2016, pp. 885-897
    Print publication:
    December 1982

  • Linear combinations of exponential distribution functions are considered, and the class of distribution functions so obtainable is investigated. Convex combinations correspond to hyperexponential distributions, while non-convex combinations yield, among other, generalized Erlang distributions obtainable as sums of independent exponential random variables with different parameters.

    For a given number n of different exponential distributions, the class investigated is an (n – 1)-dimensional convex subset of the n-dimensional real vector space generated by the n distribution functions. The geometric aspect of this subset is revealed, together with the location of hyperexponential and generalized Erlang distributions.