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1 results

  • On ratios of random variables and generalised mortality rates

  • Part of
  • Leigh A. Roberts
  • Journal:
    Journal of Applied Probability / Volume 29 / Issue 2 / June 1992
    Published online by Cambridge University Press:
    14 July 2016, pp. 268-279
    Print publication:
    June 1992

  • We find the distribution function of a ratio of dependent random variables which can represent a generalised mortality rate in a demographic or life insurance context. Each death in the numerator and each unit of exposure in the denominator are weighted by a random sum at risk, which is assumed to follow a gamma distribution. General results on the existence of moments of ratios of random variables are established, and applied to show that the moments of the rates considered here depend in a simple way on the minimum number of entrants into the mortality investigation.