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Central Limit Theorems for Uniform Model Random Polygons

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  • John Pardon

    (Princeton University)

Abstract

We show how a central limit theorem for Poisson model random polygons implies a central limit theorem for uniform model random polygons. To prove this implication, it suffices to show that in the two models, the variables in question have asymptotically the same expectation and variance. We use integral geometric expressions for these expectations and variances to reduce the desired estimates to the convergence $(1+\frac{\alpha}{n})^{n}\to e^{\alpha}$ as n→∞.

Suggested Citation

  • John Pardon, 2012. "Central Limit Theorems for Uniform Model Random Polygons," Journal of Theoretical Probability, Springer, vol. 25(3), pages 823-833, September.
    • Handle: RePEc:spr:jotpro:v:25:y:2012:i:3:d:10.1007_s10959-010-0335-2
    DOI: 10.1007/s10959-010-0335-2
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    References listed on IDEAS

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    1. W. Vervaat, 1969. "Upper bounds for the distance in total variation between the binomial or negative binomial and the Poisson distribution," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 23(1), pages 79-86, March.
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    Keywords

    Random polygons; Central limit theorem;

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