The Pareto optimality distribution

The Pareto optimality distribution Pareto optimality (sometimes known as Pareto efficiency) is an important notion in social sciences and related areas, see e.g. Klaus (2006), Chun (2005), Hild (2004), Kibris (2003), Nandeibam (2003), Papai (2001), Peris and Sanchez (2001), Brams and Fishburn (2000), Denicolo (1999), Klaus et al. (1998), Peremans et al. (1997), and Vohra (1992). This notion invariably involves the comparison of the utility of one outcome versus another, i.e. the ratio of two utilities or in general the ratio of two random variables. In this note, we derive the exact distribution of the ratio X/(X + Y) when X and Y are Pareto random variables, Pareto distribution being the first and the most popular distribution used in social sciences and related areas. Quality & Quantity Springer Journals

The Pareto optimality distribution

Loading next page...
Springer Netherlands
Copyright © 2008 by Springer Science+Business Media B.V.
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial