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A limit theorem for a certain transform of sums of independent random variables

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Summary

A certain transformation of distribution functions (d.f.'s) of positive random variables (r.v.'s) has been studied by the author and Harkness in [2] and [3]. In this paper, a limit theorem concerning such a transform of convolutions of d.f.'s is proved.

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References

  1. Loève, M. (1963).Probability Theory, D. Van Nostrand Co., Princeton.

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  2. Shantaram, R. and Harkness, W. L. (1969). Convergence of a sequence of transformations of distribution functions,Pacif. Jour. Math.,31, 403–415.

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  3. Shantaram, R. Convergence of a sequence of transformations of distribution functions—II.Pacif. Jour. Math. (to appear).

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Authors and Affiliations

  1. State University of New York, Stony Brook

    R. Shantaram & William L. Harkness

  2. Pennsylvania State University, Pennsylvania, USA

    R. Shantaram & William L. Harkness

Authors
  1. R. Shantaram
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  2. William L. Harkness
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Shantaram, R., Harkness, W.L. A limit theorem for a certain transform of sums of independent random variables. Ann Inst Stat Math 22, 181–184 (1970). https://doi.org/10.1007/BF02506334

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  • DOI: https://doi.org/10.1007/BF02506334

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