Skip to main content

On the distance between the distributions of random sums

  • Bero Roos (a1) and Dietmar Pfeifer (a2)

In this paper, we consider the total variation distance between the distributions of two random sums S M and S N with different random summation indices M and N. We derive upper bounds, some of which are sharp. Further, bounds with so-called magic factors are possible. Better results are possible when M and N are stochastically or stop-loss ordered. It turns out that the solution of this approximation problem strongly depends on how many of the first moments of M and N coincide. As approximations, we therefore choose suitable finite signed measures, which coincide with the distribution of the approximating random sum S N if M and N have the same first moments.

Corresponding author
Postal address: Fachbereich Mathematik, SPST, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany. Email address:
∗∗ Postal address: Fachbereich Mathematik, Universität Oldenburg, 26111 Oldenburg, Germany.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 7 *
Loading metrics...

Abstract views

Total abstract views: 65 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th March 2018. This data will be updated every 24 hours.