Hostname: page-component-5c6d5d7d68-xq9c7 Total loading time: 0 Render date: 2024-08-18T16:57:21.742Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Decomposition of A Class of Functions of Bounded Variation

Published online by Cambridge University Press:  20 November 2018

R. G. Laha
R. G. Laha*
Affiliation:
Catholic University, Washington, D.C.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let F1(x) and F2(x) be two distribution functions, that is, non-decreasing, right-continuous functions such that Fj(— ∞) = 0 and Fj(+ ∞) = 1 (j = 1, 2). We denote their convolution by F(x) so that

the above integrals being defined as the Lebesgue-Stieltjes integrals. Then it is easy to verify (2, p. 189) that F(x) is a distribution function. Let f1(t), f2(t), and f(t) be the corresponding characteristic functions, that is,

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 479 - 484
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Cramer, H., Ueber eine Eigenschaft der normalen Verteilungsfanktion. Math. Z., 41 (1936), 405–414.Google Scholar
2. Cramer, H., Mathematical methods of statistics (Princeton, 1946).Google Scholar
3. Linnik, Yu. V. and Skitovich, V. P., Again on a generalization of a theorem of Cramer (in Russian), Vestnik. Leningrad Univ., 13 (1958), 39–44.Google Scholar
4. Marcinkiewicz, J., Sur une propriété de la loi de Gauss, Math. Z., 44 (1938), 612–618.Google Scholar
5. Raikov, D. A., On the decomposition of Gauss and Poisson laws (in Russian), Izv. Akad. Nauk SSSR, Ser. Mat., 1 (1938), 91–124.Google Scholar
6. Widder, D. V., The Laplace Transform (Princeton, 1946).Google Scholar