Modelling large forest fires as extreme events, Northwest Sci, vol.72, pp.66-75, 1998. ,
Coherent measures of risk, Mathematical Finance, issue.9, pp.203-228, 1999. ,
Residual Life Time at Great Age, The Annals of Probability, vol.2, issue.5, pp.792-804, 1974. ,
DOI : 10.1214/aop/1176996548
On exponential representations of log-spacings of extreme order statistics, Extremes, vol.5, issue.2, pp.157-180, 2002. ,
DOI : 10.1023/A:1022171205129
Estimation of the extreme value index and regression on generalized quantile plots, Annals of Statistics, vol.11, issue.6, pp.949-970, 2005. ,
Tail index estimation and an exponential regression model, Extremes, vol.2, issue.2, pp.177-200, 1999. ,
DOI : 10.1023/A:1009975020370
Statistics of extremes: theory and applications, Wiley Series in Probability and Statistics, 2004. ,
DOI : 10.1002/0470012382
Burr regression and portfolio seg-mentation, Insurance: Mathematics and Economics, issue.23, pp.231-250, 1998. ,
Estimating the extreme value index and high quantiles with exponential regression models, Statistica Sinica, vol.13, issue.3, pp.853-880, 2003. ,
Abstract, ASTIN Bulletin, vol.10, issue.01, pp.37-58, 2001. ,
DOI : 10.2307/1427870
Excess Functions and Estimation of the Extreme-Value Index, Bernoulli, vol.2, issue.4, pp.293-318, 1996. ,
DOI : 10.2307/3318416
Regular Variation, Encyclopedia of Mathematics and its Applications, vol.27, 1987. ,
DOI : 10.1017/CBO9780511721434
An economic premium principle, Astin Bulletin Ì, issue.11 11, p.52, 1980. ,
Direct reduction of bias of the classical hill estimator, Statistical Journal, vol.3, issue.2, pp.113-136, 2005. ,
Reduced-Bias Tail Index Estimators Under a Third-Order Framework, Communications in Statistics - Theory and Methods, vol.70, issue.7, pp.1019-1040, 2009. ,
DOI : 10.1111/j.1467-842X.2004.00331.x
Bias correction in extreme value statistics with index around zero, Extremes, vol.73, issue.364, 2011. ,
DOI : 10.1007/s10687-012-0158-x
Generalzed pareto fit to the society of actuariesâlarge claims database, North American Actuarial Journal, issue.7, pp.18-36, 2003. ,
Applying the proportional hazard premium calculation principle, Astin Bulletin, issue.35, pp.409-425, 2005. ,
The optimal reinsurance strategy ??? the individual claim case, Insurance: Mathematics and Economics, vol.46, issue.3, pp.450-460, 2010. ,
DOI : 10.1016/j.insmatheco.2010.01.002
Confidence Intervals for the Tail Index, Bernoulli, vol.7, issue.5, pp.751-760, 2001. ,
DOI : 10.2307/3318540
Semi-parametric estimation for heavy tailed distributions, Extremes, vol.73, issue.364, pp.55-87, 2010. ,
DOI : 10.1007/s10687-009-0086-6
URL : https://hal.archives-ouvertes.fr/hal-00292587
La statistique face aux événements rares = statistics dealing with rare events, Pour la science, issue.385, pp.116-123, 2009. ,
Weighted Empirical and Quantile Processes, The Annals of Probability, vol.14, issue.1, pp.31-85, 1986. ,
DOI : 10.1214/aop/1176992617
Kernel Estimates of the Tail Index of a Distribution, The Annals of Statistics, vol.13, issue.3, pp.1050-1077, 1985. ,
DOI : 10.1214/aos/1176349656
Central limit theorems for sums of extreme values, Mathematical Proceedings of the Cambridge Philosophical Society, vol.86, issue.03, pp.547-558, 1985. ,
DOI : 10.1214/aos/1176343247
Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation, Journal of Multivariate Analysis, vol.76, issue.2, pp.226-248, 2001. ,
DOI : 10.1006/jmva.2000.1903
The method of moments ratio estimator for the tail shape parameter, Communications in Statistics - Theory and Methods, vol.44, issue.4, pp.711-720, 1996. ,
DOI : 10.1016/0927-5398(94)90004-3
Tail Estimates Motivated by Extreme Value Theory, The Annals of Statistics, vol.12, issue.4, pp.1467-1487, 1984. ,
DOI : 10.1214/aos/1176346804
Models for exceedances over high thresholds, Journal of the Royal Statistical Society, B, vol.52, issue.3, pp.393-442, 1990. ,
On regular variation and its application to the weak convergence of sample extremes, MMathematical Centre Tracts, vol.32, 1970. ,
Extreme Value Theory: An Introduction, Series in Operations Research and Financial Engineering, 2006. ,
DOI : 10.1007/0-387-34471-3
Comparison of tail index estimators, Statistica Neerlandica, vol.52, issue.1, pp.60-70, 1998. ,
DOI : 10.1111/1467-9574.00068
A simple asymptotic estimate for the index of a stable law, Journal of the Royal Statistical Society (B), pp.83-87, 1980. ,
On the estimation of high quantiles, Journal of Statistical Planning and Inference, vol.35, issue.1, pp.1-13, 1993. ,
DOI : 10.1016/0378-3758(93)90063-C
Almost sure convergence of the Hill estimator, Mathematical Proceedings of the Cambridge Philosophical Society, vol.44, issue.02, pp.371-381, 1988. ,
DOI : 10.2307/3214094
Laws of the iterated logarithm for sums of extreme values in the domain of attraction of a gumbel law, Bull. Sci. Math, 1989. ,
On the Estimation of the Extreme-Value Index and Large Quantile Estimation, The Annals of Statistics, vol.17, issue.4, pp.1795-1832, 1989. ,
DOI : 10.1214/aos/1176347396
A Moment Estimator for the Index of an Extreme-Value Distribution, The Annals of Statistics, vol.17, issue.4, pp.1833-1855, 1989. ,
DOI : 10.1214/aos/1176347397
Optimal Choice of Sample Fraction in Extreme-Value Estimation, Journal of Multivariate Analysis, vol.47, issue.2, pp.173-195, 1993. ,
DOI : 10.1006/jmva.1993.1078
On the estimation of the second order parameter for heavy-tailed distributions, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00634573
Reduced-bias estimator of the Proportional Hazard Premium for heavy-tailed distributions, Insurance: Mathematics and Economics, vol.52, issue.3, pp.550-559, 2013. ,
DOI : 10.1016/j.insmatheco.2013.03.010
URL : https://hal.archives-ouvertes.fr/hal-00763978
Mathématiques de lâassurance non-vie : Tarification et provisionnement, 2005. ,
Quasi-conjugate bayes estimates for gpd parameters and application to heavy tails modeling, Extremes, issue.8, pp.57-78, 2005. ,
Bias-reduced estimators of the Weibull tail-coefficient, TEST, vol.34, issue.3, pp.311-331, 2008. ,
DOI : 10.1007/s11749-006-0034-6
URL : https://hal.archives-ouvertes.fr/hal-00008881
Bias-reduced extreme quantile estimators of Weibull tail-distributions, Journal of Statistical Planning and Inference, vol.138, issue.5, pp.1389-1401, 2008. ,
DOI : 10.1016/j.jspi.2007.04.025
Bias-reduced estimators of the Weibull tail-coefficient, TEST, vol.34, issue.3, pp.311-331, 2008. ,
DOI : 10.1007/s11749-006-0034-6
URL : https://hal.archives-ouvertes.fr/hal-00008881
A new look at probability-weighted moments estimators, Serie I, pp.629-634, 2004. ,
DOI : 10.1016/j.crma.2004.02.011
Approximation of the distribution of excesses through a generalized probability-weighted moments method, Journal of Statistical Planning and Inference, vol.137, issue.3, pp.841-857, 2007. ,
DOI : 10.1016/j.jspi.2006.06.012
URL : https://hal.archives-ouvertes.fr/hal-00693666
Generalized hill's estimator, Journal of Theorical Statistic, vol.20, issue.2, pp.129-149, 2006. ,
Ratio of Generalized Hill???s estimator and its asymptotic normality theory, Mathematical Methods of Statistics, vol.18, issue.2, pp.117-133, 2009. ,
DOI : 10.3103/S1066530709020021
Refined Pickands estimators of the extreme value index, The Annals of Statistics, vol.23, issue.6, pp.2059-2080, 1995. ,
DOI : 10.1214/aos/1034713647
Selecting the optimal sample fraction in univariate extreme value estimation, Stochastic Processes and their Applications, pp.149-172, 1998. ,
DOI : 10.1016/S0304-4149(98)00017-9
Caracterisation des distributions à queues lourdes pour l'analyse des crues, 2007. ,
Estimation of extreme quantiles from heavy and light tailed distributions, Journal of Statistical Planning and Inference, vol.142, issue.10, pp.2735-2747, 2012. ,
DOI : 10.1016/j.jspi.2012.03.025
URL : https://hal.archives-ouvertes.fr/hal-00627964
Modelling of extremal events in insurance and finance, ZOR Zeitschrift f???r Operations Research Mathematical Methods of Operations Research, vol.73, issue.1, 1997. ,
DOI : 10.1007/BF01440733
On optimising the estimation of high quantiles of a probability distribution, Statistics, vol.74, issue.5, pp.401-434, 2003. ,
DOI : 10.2307/2286285
Estimating a tail exponent by modeling departure from a pareto distribution, Annals of Statistics, vol.27, pp.760-781, 1999. ,
Limiting forms of the frequency distribution of the largest or smallest member of a sample, Mathematical Proceedings of the Cambridge Philosophical Society, vol.24, issue.02, pp.180-190, 1928. ,
DOI : 10.1017/S0305004100015681
Estimation of the parameter controlling the speed of convergence in extreme value theory, Mathematical Methods of Statistics, vol.12, pp.155-176, 2003. ,
A new class of semi-parametric estimators of the second order parameter, Portugaliae Mathematica, vol.60, pp.193-214, 2003. ,
Sur la loi de probabilité de l'écart maximum, Annales de la Société Polonaise de Mathématique, vol.6, pp.93-116, 1927. ,
Conditional extremes from heavy-tailed distributions: an application to the estimation of extreme rainfall return levels, Extremes, vol.73, issue.2, pp.177-204, 2010. ,
DOI : 10.1007/s10687-010-0100-z
URL : https://hal.archives-ouvertes.fr/hal-00371757
Regular variation, extensions and tauberian theorems, cwi tract 40, center for mathematics and computer science, 1987. ,
Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire, The Annals of Mathematics, vol.44, issue.3, pp.423-453, 1943. ,
DOI : 10.2307/1968974
Kernel estimators for the second order parameter in extreme value statistics, Journal of Statistical Planning and Inference, vol.140, issue.9, pp.2632-2652, 2010. ,
DOI : 10.1016/j.jspi.2010.03.029
Estimation of the third-order parameter in extreme value statistics, TEST, vol.21, issue.2, pp.330-354, 2012. ,
DOI : 10.1007/s11749-011-0246-2
Semi-parametric estimation of the second order parameter in statistics of extremes, pp.387-414, 2002. ,
Bias reduction and explicit semi-parametric estimation of the tail index, Journal of Statistical Planning and Inference, vol.124, issue.2, pp.361-378, 2004. ,
DOI : 10.1016/S0378-3758(03)00205-2
Generalized jackknife moment estimator of the tail index, Bulletin of the International Statistical Institute, vol.58, issue.1, pp.401-402, 1999. ,
Asymptotically best linear unbiased tail estimators under a second-order regular variation condition, Journal of Statistical Planning and Inference, vol.134, issue.2, pp.409-433, 2005. ,
DOI : 10.1016/j.jspi.2004.04.013
Asymptotically unbiased estimators of the tail index based on external estimation of the second order parameter, pp.5-31, 2002. ,
Improving second order reduced bias extreme value index estimator, REVSTAT -Statistical Journal, vol.5, issue.2, pp.177-207, 2007. ,
The bootstrap methodology in statistics of extremes: theory and applications -choice of the optimal sample fraction, Extremes, vol.4, issue.4, pp.331-358, 2001. ,
DOI : 10.1023/A:1016592028871
Revisiting the Role of the Jackknife Methodology in the Estimation of a Positive Tail Index, Communications in Statistics - Theory and Methods, vol.44, issue.2, pp.319-335, 2005. ,
DOI : 10.1007/BF02127580
A note on the asymptotic variance at optimal levels of a bias-corrected Hill estimator, Statistics & Probability Letters, vol.79, issue.3, pp.295-303, 2009. ,
DOI : 10.1016/j.spl.2008.08.016
URL : https://hal.archives-ouvertes.fr/hal-00504135
Insurance premiums, 1984. ,
Théorie du risque et réassurance, 2006. ,
Kernel-type estimators for the extreme value index, Annals of Statistics, vol.31, pp.1956-1995, 2003. ,
Statistics of extremes: theory and applications, 1958. ,
How to make a Hill plot, The Annals of Statistics, vol.28, issue.1, pp.254-274, 2000. ,
DOI : 10.1214/aos/1016120372
On Asymptotic Normality of Hill's Estimator for the Exponent of Regular Variation, The Annals of Statistics, vol.13, issue.2, pp.743-756, 1985. ,
DOI : 10.1214/aos/1176349551
On some simple estimates of an exponent of regular variation, Journal of the Royal Statistical Society, vol.44, pp.37-42, 1982. ,
Adaptive Estimates of Parameters of Regular Variation, The Annals of Statistics, vol.13, issue.1, pp.331-341, 1985. ,
DOI : 10.1214/aos/1176346596
A Simple General Approach to Inference About the Tail of a Distribution, The Annals of Statistics, vol.3, issue.5, pp.1163-1174, 1975. ,
DOI : 10.1214/aos/1176343247
Parameter and Quantile Estimation for the Generalized Pareto Distribution, Technometrics, vol.4, issue.3, pp.339-1349, 1987. ,
DOI : 10.1016/0022-1694(85)90108-8
The frequency distribution of the annual maximum (or minimum) values of meteorological elements, Quarterly Journal of the Royal Meteorological Society, vol.17, issue.348, pp.158-171, 1955. ,
DOI : 10.1002/qj.49708134804
Empirical Estimation of Risk Measures and Related Quantities, North American Actuarial Journal, vol.44, issue.1, pp.44-54, 2003. ,
DOI : 10.1080/10920277.2003.10596117
The qq-estimator and heavy tails, Communications in Statistics. Stochastic Models, vol.23, issue.4, pp.699-724, 1996. ,
DOI : 10.1214/aop/1176993783
URL : https://hal.archives-ouvertes.fr/hal-00179391
Extremes and local dependence of stationnary sequences, Z. Wahr. verw. Gebiete, issue.65, pp.291-306, 1983. ,
Sur quelques estimateurs de lâindex dâune loi de Pareto : Estimation de Deheuvels Csorgo, Mason, de De Haan-Resnick et lois limites pour des sommes de valeurs extrêmes pour une variable dans le domaine de Gumbel, Thèse de Doctorat, 1986. ,
A note on the asymptotic normality of sums of extreme values. 127 ournal of Statistical Planning and Inference, pp.127-136, 1989. ,
A functional generalized hill process and applications, International Journal of Statistics and Probability, vol.1, issue.2, pp.250-268, 2012. ,
On the Generalized Hill Process for Small Parameters and Applications, Journal of Statistical Theory and Applications, vol.12, issue.1, pp.397-418, 2012. ,
DOI : 10.2991/jsta.2013.12.1.3
Sur une caract´risation empirique des extrêmes, Mathematical Reports of the Academy of Science. Canada (XIV, vol.2, issue.3, pp.89-94, 1992. ,
High quantile estimation for heavy-tailed distributions, Performance Evaluation, vol.62, issue.1-4, pp.178-192, 2005. ,
DOI : 10.1016/j.peva.2005.07.014
Laws of Large Numbers for Sums of Extreme Values, The Annals of Probability, vol.10, issue.3, pp.754-764, 1982. ,
DOI : 10.1214/aop/1176993783
Weak convergence of the hill estimator pro-cess. in j. galambos, j. lechner and simiu, editors, extreme value theory and applications ,
Estimating the extreme value in-dex and high quantiles with exponential regression models, Statistica Sinica, vol.13, pp.853-880, 2003. ,
Measuring tail thickness to estimate the stable index ? : A critique, Journal of Business & Economic Statistics, issue.15, pp.74-81, 1997. ,
Abstract, ASTIN Bulletin, vol.38, issue.01, pp.117-137, 1997. ,
DOI : 10.1111/j.1467-9574.1990.tb01526.x
Estimating the risk adjusted premium of the largest reinsurance covers, Proceeding in Compu-tational Statistics (Edited by Jaromir Antoch), pp.1577-1584, 2004. ,
Empirical estimation of the proportional hazard premium for heavy-tailed claim amounts, Insurance: Mathematics and Economics, vol.45, issue.1, pp.49-58, 2009. ,
DOI : 10.1016/j.insmatheco.2009.03.004
Statistical estimate of the proportional hazard premium of loss, Scandinavian Actuarial Journal, issue.3, pp.147-161, 2007. ,
Asymptotically unbiased estimators for the extreme-value index, Statistics & Probability Letters, vol.38, issue.2, pp.107-115, 1998. ,
DOI : 10.1016/S0167-7152(97)00160-0
Statistical inference using extreme order statistics, Annals of Statistics, vol.3, issue.1, pp.119-131, 1975. ,
Statistical analysis of extreme values, 2001. ,
DOI : 10.1007/978-3-0348-6336-0
Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields, Birkh Ìuser, 1997. ,
Abstract, ASTIN Bulletin, vol.29, issue.02, pp.339-349, 1999. ,
DOI : 10.1007/978-1-4613-3638-9_7
Extreme Values, regular Variation, and Point Process, 1987. ,
Consistency of hill's estimator for dependent data, Journal of Applied Probability, issue.32, pp.139-167, 1995. ,
Extreme value statistics and wind storm losses: A case study, Scandinavian Actuarial Journal, vol.2, issue.1, pp.70-94, 1997. ,
DOI : 10.1214/ss/1177012400
Comparison of estimation methods in extreme value theory, Communications in Statistics - Theory and Methods, vol.47, issue.4, pp.759-773, 1996. ,
DOI : 10.2307/2286285
ON LEAST SQUARES ESTIMATES OF AN EXPONENTIAL TAIL COEFFICIENT, Statistics & Risk Modeling, vol.14, issue.4, pp.353-372, 1996. ,
DOI : 10.1524/strm.1996.14.4.353
Empirical Processes with Applications to Statistics, 1986. ,
DOI : 10.1137/1.9780898719017
Estimating Tails of Probability Distributions, The Annals of Statistics, vol.15, issue.3, pp.1174-1207, 1987. ,
DOI : 10.1214/aos/1176350499
A contribution to the estimation of the tail index of heavy-tailed distributions. phd. thesis, university of michigan, 2002. ,
A simulation study on the performance of extremevalue index estimators and proposed robustifying modifications, 5th Hellenic Eu-ropean Conference on Computer Mathematics and its Applications, pp.847-852, 2001. ,
Stochastic musings : Perspectives from the pioneers of the late 20th century, Laurence Erlbaum, pp.141-160, 2003. ,
Cours dâAnalyse Math´matique : Th´orie des fonctions, 1990. ,
Weak Convergence and Empirical Processes. With Applications to Statistics, 1996. ,
On univariate extreme value statistics and the estimation of reinsurance premiums, Insurance: Mathematics and Economics, vol.38, issue.3, pp.441-459, 2006. ,
DOI : 10.1016/j.insmatheco.2005.11.002
Limit theorems for linear combinations of extreme values with applications to inference about the tail of a distribution, Acta Scientiarum Mathematicarum, vol.60, pp.761-777, 1995. ,
La distribution de la plus grande de n valeurs, Revue de Mathématique Union Interbalcanique, issue.1, pp.141-160, 1936. ,
Insurance pricing and increased limits ratemaking by proportional hazards transforms, Insurance: Mathematics and Economics, vol.17, issue.1, pp.43-54, 1995. ,
DOI : 10.1016/0167-6687(95)00010-P
Abstract, ASTIN Bulletin, vol.50, issue.01, pp.71-92, 1996. ,
DOI : 10.2143/AST.21.2.2005365
URL : https://hal.archives-ouvertes.fr/hal-00953003
Estimation of parameters and large quantiles based on the k-largest observations, Journal of the American Statistical Association, vol.73, issue.364, pp.812-815, 1978. ,
Estimation of second order parameters using probability weighted moments, ESAIM: Probability and Statistics, 2011. ,
DOI : 10.1051/ps/2010017
URL : https://hal.archives-ouvertes.fr/hal-00365305
The Dual Theory of Choice under Risk, Econometrica, vol.55, issue.1, pp.95-115, 1987. ,
DOI : 10.2307/1911158