The final estimator is the sample mean of the likelihood ratios multiplied by the rare-event indicator. It is computed by drawing samples from the fitted Normal proposal, calculating the ratio of the standard normal density to the proposal density, multiplying by the indicator that the sample exceeds γ, and averaging the results.
Conditions: Samples are drawn from the fitted Normal proposal, not the original distribution.; The event indicator is 1{Zj>γ}.
The final estimator is the sample mean of the likelihood ratios multiplied by the rare-event indicator. It is computed by drawing samples from the fitted Normal proposal, calculating the ratio of the standard normal density to the proposal density, multiplying by the indicator that the sample exceeds γ, and averaging the results.
Conditions: Samples are drawn from the fitted Normal proposal, not the original distribution.; The event indicator is 1{Zj>γ}.
The confidence interval is constructed as a symmetric interval around the point estimate. The half-width is calculated by multiplying 1.96 by the sample standard deviation of the weighted estimator array, and then dividing by the square root of the number of proposal samples.
Conditions: Uses the sample standard deviation of the weighted estimates.; The interval is presented as a numerical summary based on a normal approximation.
The confidence interval is constructed as a symmetric interval around the point estimate. The half-width is calculated by multiplying 1.96 by the sample standard deviation of the weighted estimator array, and then dividing by the square root of the number of proposal samples.
Conditions: Uses the sample standard deviation of the weighted estimates.; The interval is presented as a numerical summary based on a normal approximation.