5.13 Population Distribution Compared to Bootstrap Distribution

BUT, for real data, we cannot generate new samples from the true population!
Use the bootstrap

The distribution of the mean of alpha is shown on the left, with 1000 samples generated from the true population. A bootstrap distribution is shown in the middle, with 1000 samples taken from the original sample. Note that both confidence intervals contain the true alpha (pink line) in the right panel, and that the spread of both distributions is similar.

Figure 5.7: The distribution of the mean of alpha is shown on the left, with 1000 samples generated from the true population. A bootstrap distribution is shown in the middle, with 1000 samples taken from the original sample. Note that both confidence intervals contain the true alpha (pink line) in the right panel, and that the spread of both distributions is similar.

The 2 distributions look very similar with comparable estimates for \({\alpha}\)