Estimation of rare event probability is a key issue of recent simulation literature. This topic is of major importance in queuing systems as well as extreme value analysis in many fields such as reliability, telecommunication and insurance risks. However, estimating rare events is a challenging problem from a methodological point of view: since, analytical computation of rare event probabilities can be achieved only for very simple distribution, Monte Carlo approximation have been proposed. In this paper, after a brief review of some recent literature, we propose an alternative method for estimating rare events using simulation: we propose a simple deterministic transform of the random sample drawn from the original distribution such that the rare events become not-so-rare. The new approach can be easily implemented and the resulting estimator can achieve a bounded relative error in some relevant cases such as exponential-like and regularly varying functions. The approach is presented here in a very simple basic setting of a single random variable but it can be also extended to sum of random variables.

Alternative rare events probability estimation / Arima, Serena; Giovanni, Petris; Tardella, Luca. - ELETTRONICO. - (2010), pp. 1-8. (Intervento presentato al convegno 45th Scientific Meeting of the Italian Statistical Society tenutosi a Padova nel 29 giugno - 1 luglio 2010).

Alternative rare events probability estimation

ARIMA, SERENA;TARDELLA, Luca
2010

Abstract

Estimation of rare event probability is a key issue of recent simulation literature. This topic is of major importance in queuing systems as well as extreme value analysis in many fields such as reliability, telecommunication and insurance risks. However, estimating rare events is a challenging problem from a methodological point of view: since, analytical computation of rare event probabilities can be achieved only for very simple distribution, Monte Carlo approximation have been proposed. In this paper, after a brief review of some recent literature, we propose an alternative method for estimating rare events using simulation: we propose a simple deterministic transform of the random sample drawn from the original distribution such that the rare events become not-so-rare. The new approach can be easily implemented and the resulting estimator can achieve a bounded relative error in some relevant cases such as exponential-like and regularly varying functions. The approach is presented here in a very simple basic setting of a single random variable but it can be also extended to sum of random variables.
2010
45th Scientific Meeting of the Italian Statistical Society
importance sampling; rare event simulation; bounded relative error; monte carlo methods; heavy tails; statistical computing
04 Pubblicazione in atti di convegno::04b Atto di convegno in volume
Alternative rare events probability estimation / Arima, Serena; Giovanni, Petris; Tardella, Luca. - ELETTRONICO. - (2010), pp. 1-8. (Intervento presentato al convegno 45th Scientific Meeting of the Italian Statistical Society tenutosi a Padova nel 29 giugno - 1 luglio 2010).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/355158
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