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The parameters of the Normal proposal distribution are chosen using maximum likelihood estimation. The mean $\mu$ is set to the sample mean of the retained $g^*$ samples, and the standard deviation $\sigma$ is set to the square root of the sample second central moment of those samples.

Conditions: The proposal family is restricted to Normal distributions.; The data used for fitting are the retained samples satisfying $X>\gamma$.

The parameters of the Normal proposal distribution are chosen using maximum likelihood estimation. The mean $\mu$ is set to the sample mean of the retained $g^*$ samples, and the standard deviation $\sigma$ is set to the square root of the sample second central moment of those samples.

Conditions: The proposal family is restricted to Normal distributions.; The data used for fitting are the retained samples satisfying $X>\gamma$.

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 $\gamma$, and averaging the results.

Conditions: Samples are drawn from the fitted Normal proposal, not the original distribution.; The event indicator is $\mathbf{1}_{\{Z_j>\gamma\}}$.

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 $\gamma$, and averaging the results.

Conditions: Samples are drawn from the fitted Normal proposal, not the original distribution.; The event indicator is $\mathbf{1}_{\{Z_j>\gamma\}}$.