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Approximating Perpetuities

Author

Listed:
  • Margarete Knape

    (J.W. Goethe-University Frankfurt a.M.)

  • Ralph Neininger

    (J.W. Goethe-University Frankfurt a.M.)

Abstract

We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the perpetuity. We significantly reduce the complexity of the earlier algorithm. Also one particular perpetuity arising in the analysis of the selection algorithm Quickselect is studied in more detail. Our approach works well for distribution functions. For densities we have weaker error bounds although computer experiments indicate that densities can also be approximated well.

Suggested Citation

  • Margarete Knape & Ralph Neininger, 2008. "Approximating Perpetuities," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 507-529, December.
    • Handle: RePEc:spr:metcap:v:10:y:2008:i:4:d:10.1007_s11009-007-9059-x
    DOI: 10.1007/s11009-007-9059-x
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    References listed on IDEAS

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    1. Devroye, Luc & Letac, Gerard & Seshadri, Vanamamalai, 1986. "The limit behavior of an interval splitting scheme," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 183-186, June.
    2. Luc Devroye, 2001. "Simulating Perpetuities," Methodology and Computing in Applied Probability, Springer, vol. 3(1), pages 97-115, March.
    3. Chen, Robert & Goodman, Richard & Zame, Alan, 1984. "Limiting distributions of two random sequences," Journal of Multivariate Analysis, Elsevier, vol. 14(2), pages 221-230, April.
    4. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
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    Cited by:

    1. S. Valère Bitseki Penda & Jean-François Delmas, 2023. "Central Limit Theorem for Kernel Estimator of Invariant Density in Bifurcating Markov Chains Models," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1591-1625, September.

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