Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-06-08T16:52:38.146Z Has data issue: false hasContentIssue false
  • English
  • Français

Subexponential distribution functions

Published online by Cambridge University Press:  09 April 2009

E. J. G. Pitman
E. J. G. Pitman
Affiliation:
301 Davey St Hobart, Tasmania 7000, Australia
Rights & Permissions [Opens in a new window]

Abstract

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.

A distribution function (F on [0,∞) belongs to the subexponential class if and only if 1−F(2) (x) ~ 2(1−F(x)), as x→ ∞. For an important class of distribution functions, a simple, necessary and sufficient condition for membership of is given. A comparison theorem for membership of and also some closure properties of are obtained.

1980 Mathematics subject classification (Amer. Math. Soe.): primary 60 E 05; secondary 60 J 80.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 3 , May 1980 , pp. 337 - 347
Copyright
Copyright © Australian Mathematical Society 1980

References

Athreya, K. B. and Ney, P. E. (1972), Branching processes (Springer-Verlag, Berlin).CrossRefGoogle Scholar
Chistyakov, V. P. (1964), ‘A theorem on sums of independent positive random variables and its applications to branching random processes’, Theory Prob. and Appl. 9, 640–648.CrossRefGoogle Scholar
Chover, J., Ney, P. E. and Wainger, S. (1974), ‘Degeneracy properties of subcritical branching processes’, Ann. Probability 1, 663–673.Google Scholar
Pakes, A. G. (1975), ‘On the tails of waiting-time distributions’, J. Appl. Prob. 12, 555–564.CrossRefGoogle Scholar
Teugels, J. L. (1975), ‘The class of subexponential distributions’, Ann. Probability 3, 1000–1011.CrossRefGoogle Scholar