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Susan Vanderplas
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Fix rendering issues
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_freeze/part-advanced-topics/01-simulation/execute-results/html.json

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part-advanced-topics/01-simulation.qmd

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Simulation from different distributions can be used to determine which estimators are most appropriate for a given scenario, to determine how likely it is to observe a specific value in a sample of size $n$, and for many other applications.
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### Example: Mean vs. Median
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How can you use this information to determine which estimator is preferable in each $\nu, n$ situation?
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#### R
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Considering the results we obtained, it seems clear that when we have a very low ($\nu<=5$) degrees of freedom, the median is a preferable estimator because it has lower variance; when we have a higher number of degrees of freedom, the mean is a preferable estimator on the basis of variance.
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Both estimators are asymptotically unbiased, and are unbiased even for small sample sizes when the distribution is symmetric.
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## Simulation to test model assumptions
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