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Limit distribution of a roundoff error

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  • Shimura, Takaaki

Abstract

Let [X] and {X} be the integer and the fractional parts of a random variable X. The conditional distribution function Fn(x)=P({X}≤x|[X]=n) for an integer n is investigated. Fn for a large n is regarded as the distribution of a roundoff error in an extremal event. For most well-known continuous distributions, it is shown that Fn converges as n→∞ and three types of limit distributions appear as the limit distribution according to the tail behavior of F.

Suggested Citation

  • Shimura, Takaaki, 2012. "Limit distribution of a roundoff error," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 713-719.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:4:p:713-719
    DOI: 10.1016/j.spl.2011.12.021
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    References listed on IDEAS

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    1. F.W. Steutel & J.G.F. Thiemann, 1989. "On the independence of integer and fractional parts," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 43(1), pages 53-59, March.
    2. Lih–Yuan Deng & Raj S. Chhikara, 1990. "On the characterization of the exponential distribution by the independence of its integer and fractional parts," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 44(2), pages 83-85, June.
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