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Decomposition of weakly aging distributions

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Abstract

A class of weakly aging distribution functions is introduced and a number of properties of this class are derived. It is proved in particular that a random variable ξ, having a weakly aging distribution function, can be written as a sum of two independent random variables, one of which has exponential distribution with a parameter equal to the modulus of the singular point of Me−sξ nearest the coordinate origin.

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Literature cited

  1. R. Barlow and F. Proshan, Mathematical Theory of Reliability [in Russian], Sov. Radio, Moscow (1967).

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  2. A. D. Solov'ev, “Asymptotic distribution of the moment of first crossing of a high level by a birth and death process,” Proceedings of the Sixth Berkeley Symposium on Mathematical and Statistical Probability, Vol. III (1970).

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Moscow

    O. P. Vinogradov

Authors
  1. O. P. Vinogradov
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Translated from Matematicheskie Zametki, Vol. 22, No. 4, pp. 571–574, October, 1977.

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Vinogradov, O.P. Decomposition of weakly aging distributions. Mathematical Notes of the Academy of Sciences of the USSR 22, 809–811 (1977). https://doi.org/10.1007/BF01146429

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  • DOI: https://doi.org/10.1007/BF01146429

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