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2 results

  • A multivariate IFR class

  • Thomas H. Savits
  • Journal:
    Journal of Applied Probability / Volume 22 / Issue 1 / March 1985
    Published online by Cambridge University Press:
    14 July 2016, pp. 197-204
    Print publication:
    March 1985

  • A non-negative random vector T is said to have a multivariate increasing failure rate distribution (MIFR) if and only if E[h(x, T)] is log concave in x for all functions h(x, t) which are log concave in (x, t) and are non-decreasing and continuous in t for each fixed x. This class of distributions is closed under deletion, conjunction, convolution and weak limits. It contains the multivariate exponential distribution of Marshall and Olkin and those distributions having a log concave density. Also, it follows that if T is MIFR and ψ is non-decreasing, non-negative and concave then ψ (T) is IFR.