Parametric Models and Their Tails
In this chapter we consider approaches to selecting a parametric family of distributions for a random variable and approaches to estimating the parameters. We also present techniques for analyzing the tails of the chosen probability distribution and the effect of the tails on the estimation of risk measures. Finally, we consider a semiparametric approach to the estimation of tail probabilities. It provides an alternative to relying on a full parametric model in order to produce estimates of tail probabilities beyond the range of the sample data.
- 9.Casella, G., Berger, R.L.: Statistical Inference, 2nd edn. Duxbury Press, Belmont (2002)Google Scholar
- 13.Embrechts, P., Klüppelberg, C., Mikosch, T.: Modelling Extremal Events for Insurance and Finance. Springer, New York (1997)Google Scholar
- 20.de Haan, L., Ferreira, A.: Extreme Value Theory: An Introduction. Springer, New York (2006)Google Scholar
- 33.Meucci, A.: Risk and Asset Allocation. Springer, New York (2005)Google Scholar
- 37.Resnick, S.I.: Heavy-Tail Phenomena: Probabilistic and Statistical Modeling. Springer, New York (2007)Google Scholar