Horvitz–Thompson Unequal Sampling

The Horvitz-Thompson estimator provides an unbiased estimate of a finite population total when elements are sampled with unequal probabilities. Instead of treating each sample unit equally, we weight each unit by the inverse of its inclusion probability. This ensures that units less likely to be selected contribute proportionately more when they do appear, balancing the expected value across all possible samples.

Experiment

Use the Horvitz–Thompson Estimator module to interact with different finite population values and sampling designs.

1. Set the Design control to "Unequal".
2. Set Value 1 to 1, Value 2 to 2, and Value 3 to 3.
3. Set the Selected unit to 3 to see the realization if the third unit is drawn.
4. Observe that the selected HT Estimate is 18.0, but the overall HT Expectation remains exactly 6.0.
5. Change the Design to "Uniform" and observe how all inclusion probabilities become 1/3, and the variance drops to 0 if all values are equal.