## Abstract

The tail probability of a function of a multivariate random variable is not easy to estimate by the crude Monte Carlo simulation. When the occurrence of the function value over a threshold is rare, the accurate estimation of the corresponding probability requires a huge number of samples. When the explicit form of the cumulative distribution function of each component of the variable is known, the inverse transform likelihood ratio method is directly applicable scheme to estimate the tail probability efficiently. The method is a type of the importance sampling and its efficiency depends on the selection of the importance sampling distribution. When the cumulative distribution of the multivariate random variable is represented by a copula and its marginal distributions, we develop an iterative algorithm to find the optimal importance sampling distribution, and show the convergence of the algorithm. The performance of the proposed scheme is compared with the crude Monte Carlo simulation numerically.

Original language | English |
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Pages (from-to) | 65-85 |

Number of pages | 21 |

Journal | Communications for Statistical Applications and Methods |

Volume | 31 |

Issue number | 1 |

DOIs | |

State | Published - 2024 |

## Keywords

- Monte Carlo simulation
- copula
- importance sampling
- inverse transform likelihood ratio method
- rare event simulation