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A Simple General Approach to Inference About the Tail of a Distribution
Open accessAbstract
A simple general approach to inference about the tail behavior of a distribution is proposed. It is not required to assume any global form for the distribution function, but merely the form of behavior in the tail where it is desired to draw inference. Results are particularly simple for distributions of the Zipf type, i.e., where $G(y) = 1 - Cy^{-\alpha}$ for large $y$. The methods of inference are based upon an evaluation of the conditional likelihood for the parameters describing the tail behavior, given the values of the extreme order statistics, and can be implemented from both Bayesian and frequentist viewpoints.
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Citations
Cited by
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Clauset, A., Shalizi, C. R., & Newman, M. E. J. (2009) · SIAM Review · doi:10.1137/070710111 · Cited by 8,019
Power Laws in Economics and Finance
Gabaix, X. (2009) · Annual Review of Economics · doi:10.1146/annurev.economics.050708.142940 · Cited by 907
The econometrics of financial markets
Pagan, A. (1996) · Journal of Empirical Finance · doi:10.1016/0927-5398(95)00020-8 · Cited by 873
Value-at-Risk Prediction: A Comparison of Alternative Strategies
Kuester, K. (2005) · Journal of Financial Econometrics · doi:10.1093/jjfinec/nbj002 · Cited by 632
Estimation of Parameters and Large Quantiles Based on the k Largest Observations
Weissman, I. (1978) · Journal of the American Statistical Association · doi:10.1080/01621459.1978.10480104 · Cited by 462
Metadata
- Authors
- Hill, B. M.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1975-09-01
- Volume
- 3
- Issue
- 5
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2048649579
- Cited by
- 3,086
- References
- 0
- FWCI
- 1.77
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Hill, B. M. (1975). A Simple General Approach to Inference About the Tail of a Distribution. The Annals of Statistics. https://doi.org/10.1214/aos/1176343247
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