1
Sampling distributions and Monte
Carlo experiments
Generate artificial data samples from known probability
distribution
Each experiment (‘replication’) is a sample of N
primitive experiments
We can establish sampling distribution of statistics
experimentally –
this is useful if the sampling
distribution cannot be derived theoretically
Hence it is particularly useful for non-normal parent
distributions or statistics which are non-linear
functions of data
The technique can be used for other statistics - eg
rejection probabilities
Estimating the mean
Theoretical value
Experimental value
Sample size 100
Mean
0
.0000586
Standard deviation
0.1
.0997881
Sample size 1000
Mean
0
.0004816
Standard deviation
0.03162
.0320018
Sampling distribution of the Mean: 100 observations
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
Experiment
Theory

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