Statistical inference for the generalized Pareto distribution: Maximum likelihood revisited

Communications in Statistics - Theory and Methods

Volumn 35, Issue 5, 2006, Pages 785-802

  Chaouche, Ali ^a   Bacro, Jean Noël ^b,c  

^a AGROPARISTECH   (France)

^b UNIV MONTPELLIER   (France)

^c UNIVERSITÉ DE MONTPELLIER   (France)

Author keywords

Generalized Pareto distribution; Maximum likelihood estimation; Shape parameter test

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; FAILURE ANALYSIS; MAXIMUM LIKELIHOOD ESTIMATION; OPTIMIZATION; PARAMETER ESTIMATION;

CONVERGENCE FAILURE; GENERALIZED PARETO DISTRIBUTION; SCALE PARAMETERS; SHAPE PARAMETER TEST;

STATISTICAL METHODS;

EID: 33646949295     PISSN: 03610926     EISSN: 1532415X     Source Type: Journal    
DOI: 10.1080/03610920500501429     Document Type: Article

References (11)

1. Balkema, A. A., de Haan, L. (1974). Residual lifetime at great age. Ann. Probab. 2:792-804.
2. Castillo, E., Hadi, A. (1997). Fitting the generalized Pareto distribution to data. J. Amer. Statist. Assoc. 92:1609-1620.
3. Chaouche, A., Bacro, J. N. (2004). A statistical test procedure for the shape parameter of a generalized Pareto distribution. Comp. Stat. Data Anal. 45:787-803.
4. Davison, A. C., Smith, R. L. (1990). Models for exceedances over high thresholds. J. R. Statist. Soc. B 52(3):393-442.
5. Embrechts, P., Klüppelberg, C., Mikosch, T. (1997). Modelling Extremal Events. Springer.
6. Hosking, J. R. M., Wallis, J. R. (1987). Parameter and quantile estimation for the generalized Pareto distribution. Technometrics 29:339-349.
7. Pickands, J. (1975). Statistical inference using extreme order statistics. Ann. Stat. 3:119-131.
8. Rasmussen, P. F. (2001). Generalized probability weighted moments: application to the generalized Pareto distribution. Water Resour. Res. 37(6):1745-1751.
9. Salvadori, G. (2002). Linear combinations of order statistics to estimate the position and scale parameters of the generalized Pareto distribution. Stochastic Environ. Res. Risk Assess. 16:1-17.
10. Smith, R. L. (1985). Maximum likelihood estimation in a class of non-regular cases. Biometrika 72:67-90.
11. Smith, R. L. (1987). Estimating tails of probability distributions. Ann. Statist. 3(15): 1174-1207.