Further comments on the continuity of distribution functions obtained by superposition
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- by Barthel W. Huff PDF
- Proc. Amer. Math. Soc. 35 (1972), 561-564 Request permission
Abstract:
Let $\{ X(t)\}$ be a differential process with discontinuous distributions and Y a nonnegative random variable independent of the process. The superposition $X(Y)$ has a continuous probability distribution if and only if the process has nonzero trend term and Y has continuous distribution. The nature of discontinuities of the probability distribution of the superposition is indicated.References
- Barthel W. Huff, Comments on the continuity of distribution functions obtained by superposition, Proc. Amer. Math. Soc. 27 (1971), 141–146. MR 270417, DOI 10.1090/S0002-9939-1971-0270417-9
- Eugene Lukacs, Characteristic functions, Griffin’s Statistical Monographs & Courses, No. 5, Hafner Publishing Co., New York, 1960. MR 0124075
- Howard G. Tucker, A graduate course in probability, Probability and Mathematical Statistics, Vol. 2, Academic Press, Inc., New York-London, 1967. MR 0221541
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 561-564
- MSC: Primary 60E05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0303574-7
- MathSciNet review: 0303574