New Methods for Estimating Tail Probabilities and Extreme Value Disributions.
Abstract
This research has focused on the problem of estimating probabilities in the upper tail of an underlying distribution and the corresponding quantiles based on a random sample from the distribution. Two estimation procedures, exponential tail and transformed exponential tail, were defined and their bias and variance properties were thoroughly studied both analytically and by means of an extensive Monte Carlo experiment. The experiment involved several forms of each of the two procedures; twenty underlying distributions were simulated, including a variety of Weibull and lognormal distributions; four sample sizes were considered--100, 200, 400 and 800. Careful study of the analytic and Monte Carlo results showed that exponential tail and transformed exponential tail procedures worked quite well, but indicated a potential for substantial further improvement by properly combining them. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 14, 1979
- Accession Number
- ADA080446
Entities
People
- Charles J. Stone
- John D. Gins
- Leo Breiman
Organizations
- Technology Service Corporation