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The zero-variance density $g^*$ is the conditional distribution of the random variable $X$ given that the rare event $X>\gamma$ occurs. It is the ideal importance-sampling proposal that would make the estimator have zero variance.

Conditions: The target quantity is the rare-event probability $P(X>\gamma)$.; $g^*$ is supported only on the region $x>\gamma$.

The zero-variance density $g^*$ is the conditional distribution of the random variable $X$ given that the rare event $X>\gamma$ occurs. It is the ideal importance-sampling proposal that would make the estimator have zero variance.

Conditions: The target quantity is the rare-event probability $P(X>\gamma)$.; $g^*$ is supported only on the region $x>\gamma$.