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Statistical Aspects of Perpetuities

✍ Scribed by Rudolf Grübel; Susan M Pitts

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
161 KB
Volume
75
Category
Article
ISSN
0047-259X

No coin nor oath required. For personal study only.

✦ Synopsis

For a distribution + on the unit interval we define the associated perpetuity 9( +)

a sequence of independent random variables with distribution +. Such quantities arise in insurance mathematics and in many other areas. We prove the differentiability of the perpetuity functional 9 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.

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