On the efficient simulation of the left-tail of the sum of correlated log-normal variates
-
Mohamed-Slim Alouini
,
Abla Kammoun
Abstract
The sum of log-normal variates is encountered in many challenging applications such as performance analysis of wireless communication systems and financial engineering. Several approximation methods have been reported in the literature. However, these methods are not accurate in the tail regions. These regions are of primordial interest as small probability values have to be evaluated with high precision. Variance reduction techniques are known to yield accurate, yet efficient, estimates of small probability values. Most of the existing approaches have focused on estimating the right-tail of the sum of log-normal random variables (RVs). Here, we instead consider the left-tail of the sum of correlated log-normal variates with Gaussian copula, under a mild assumption on the covariance matrix. We propose an estimator combining an existing mean-shifting importance sampling approach with a control variate technique. This estimator has an asymptotically vanishing relative error, which represents a major finding in the context of the left-tail simulation of the sum of log-normal RVs. Finally, we perform simulations to evaluate the performances of the proposed estimator in comparison with existing ones.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Probability distribution of the life time of a drift-diffusion-reaction process inside a sphere with applications to transient cathodoluminescence imaging
- A quasi-Monte Carlo implementation of the ziggurat method
- On the efficient simulation of the left-tail of the sum of correlated log-normal variates
- Bayesian estimation of ordinary differential equation models when the likelihood has multiple local modes
- On the modeling of linear system input stochastic processes with given accuracy and reliability
- Remarks on randomization of quasi-random numbers
- On average dimensions of particle transport estimators
Articles in the same Issue
- Frontmatter
- Probability distribution of the life time of a drift-diffusion-reaction process inside a sphere with applications to transient cathodoluminescence imaging
- A quasi-Monte Carlo implementation of the ziggurat method
- On the efficient simulation of the left-tail of the sum of correlated log-normal variates
- Bayesian estimation of ordinary differential equation models when the likelihood has multiple local modes
- On the modeling of linear system input stochastic processes with given accuracy and reliability
- Remarks on randomization of quasi-random numbers
- On average dimensions of particle transport estimators
