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Computing

, Volume 43, Issue 4, pp 401–410 | Cite as

Yet another application of a binomial recurrence order statistics

  • W. Szpankowski
  • V. Rego
Article

Abstract

We investigate the moments of the maximum of a set of i.i.d geometric random variables. Computationally, the exact formula for the moments (which does not seem to be available in the literature) is inhibited by the presence of an alternating sum. A recursive expression for the moments is shown to be superior. However, the recursion can be both computationally intensive as well as subject to large round-off error when the set of random variables is large, due to the presence of factorial terms. To get around this difficulty we develop accurate asymptotic expressions for the moments and verify our results numerically.

Key words

geometric distribution order statistics binomial recurrence asymptotic approximation program unification concurrency enhancement 

Eine weitere Anwendung binomischer Rekurrenz. Orderstatistik

Zusammenfassung

Wir untersuchen die Momente des Maximums einer Menge von unabhängig identisch verteilten geometrischen Zufallsvariablen. Numerisch ist die Verwendung der exakten Formel für die Momente (die überdies in der Literatur nicht erscheint) wegen des Vorhandenseins einer alternierenden Summe nicht ratsam. Ein rekursiver Ausdruck für die Momente ist besser geeignet. Jedoch kann die Rekursion wegen des Auftretens von faktoriellen Ausdrücken sowohl viel Rechenaufwand erfordern als auch große Rundungsfehler verursachen, wenn die Menge der Zufallsvariablen groß ist. Zur Überwindung dieser Schwierigkeiten entwickeln wir genaue asymptotische Formeln für die Momente und verifizieren unsere Ergebnisse numerisch.

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References

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • W. Szpankowski
    • 1
  • V. Rego
    • 1
  1. 1.Department of Computer SciencesPurdue UniversityWest LafayetteUSA

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