caa a22 4500 605520003 CHVBK 20210128100733.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s11009-013-9371-6 doi (NATIONALLICENCE)springer-10.1007/s11009-013-9371-6 Error Rates and Improved Algorithms for Rare Event Simulation with Heavy Weibull Tails [Elektronische Daten] [Søren Asmussen, Dominik Kortschak] Let Y 1,...,Y n be i.i.d. subexponential and S n  = Y 1 + ⋯ + Y n . Asmussen and Kroese (Adv Appl Probab 38:545-558, 2006) suggested a simulation estimator for evaluating ${\mathbb P}(S_n>x)$ , combining an exchangeability argument with conditional Monte Carlo. The estimator was later shown by Hartinger and Kortschak (Bl DGVFM 30:363-377, 2009) to have vanishing relative error. For the Weibull and related cases, we calculate the exact error rate and suggest improved estimators. These improvements can be seen as control variate estimators, but are rather motivated by second order subexponential theory which is also at the core of the technical proofs. Springer Science+Business Media New York, 2013 Complexity nationallicence Conditional Monte Carlo nationallicence Control variates nationallicence Lognormal distribution nationallicence M/G/1 queue nationallicence Pollaczeck-Khinchine formula nationallicence Rare event nationallicence Regular variation nationallicence Ruin theory nationallicence Second order subexponentiality nationallicence Subexponential distribution nationallicence Vanishing relative error nationallicence Weibull distribution nationallicence Asmussen Søren Department of Mathematics, Aarhus University, Ny Munkegade, 8000, Aarhus C, Denmark aut Kortschak Dominik Laboratoire SAF, Institut de Science Financière et d'Assurances, Université Lyon 1, 50 Avenue Tony Garnier, 69007, Lyon, France aut Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/2(2015-06-01), 441-461 1387-5841 17:2<441 2015 17 11009 https://doi.org/10.1007/s11009-013-9371-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9371-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Asmussen Søren Department of Mathematics, Aarhus University, Ny Munkegade, 8000, Aarhus C, Denmark aut NATIONALLICENCE 700 1- Kortschak Dominik Laboratoire SAF, Institut de Science Financière et d'Assurances, Université Lyon 1, 50 Avenue Tony Garnier, 69007, Lyon, France aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/2(2015-06-01), 441-461 1387-5841 17:2<441 2015 17 11009