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Statistical Aspects of Perpetuities

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  • Grübel, Rudolf
  • Pitts, Susan M.

Abstract

For a distribution [mu] on the unit interval we define the associated perpetuity [Psi]([mu]) as the distribution of 1+X1+X1X2+X1X2X3+..., where (Xn)n[set membership, variant] is a sequence of independent random variables with distribution [mu]. Such quantities arise in insurance mathematics and in many other areas. We prove the differentiability of the perpetuity functional[psi] with respect to integral and supremum norms. These results are then used to investigate the statistical properties of empirical perpetuities, including the behaviour of bootstrap confidence regions.

Suggested Citation

  • Grübel, Rudolf & Pitts, Susan M., 2000. "Statistical Aspects of Perpetuities," Journal of Multivariate Analysis, Elsevier, vol. 75(1), pages 143-162, October.
    • Handle: RePEc:eee:jmvana:v:75:y:2000:i:1:p:143-162
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    References listed on IDEAS

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    1. S. Pitts, 1994. "Nonparametric estimation of compound distributions with applications in insurance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(3), pages 537-555, September.
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