Recurrence Relations

  • Kenneth Lange
Part of the Statistics and Computing book series (SCO)


Recurrence relations are ubiquitous in computational statistics and probability. Devising good recurrence relations is both an art and a science. One general theme is the alpha and omega principle; namely, most recurrences are derived by considering either the first or last event in a chain of events. The following examples illustrate this principle and some other commonly employed techniques.


Recurrence Relation Candidate Position Recursive Method Recursive Scheme Quick Sort Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Barbour AD, Holst L, Janson S (1992) Poisson Approximation. Oxford University Press, OxfordMATHGoogle Scholar
  2. 2.
    Henrici P (1982) Essentials of Numerical Analysis with Pocket Calculator Demonstrations. Wiley, New YorkMATHGoogle Scholar
  3. 3.
    Kolchin VF, Sevast’yanov BA, Chistyakov VP (1978) Random Allocations. Winston, Washington DCGoogle Scholar
  4. 4.
    Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. Cambridge University Press, CambridgeGoogle Scholar
  5. 5.
    Sandell D (1991) Computing probabilities in a generalized birthday problem. Math Scientist 16:78-82MATHMathSciNetGoogle Scholar
  6. 6.
    Wilf HS (1986) Algorithms and Complexity. Prentice-Hall, New YorkMATHGoogle Scholar

Copyright information

© Springer New York 2010

Authors and Affiliations

  1. 1.Departments of Biomathematics, Human Genetics, and Statistics David Geffen School of MedicineUniversity of California, Los AngelesLos AngelesUSA

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