# Normal Location and Scale

This litte application sends the y-coordinates of the points which are normal distributed (pseudo-)random numbers to the server.
There, location and scale of the sample are estimated using the Statistics software R.
The return values are plotted and displayed.

The computed estimates are:

• mean, standard deviation: red (non-robust!)
• median and MAD: black (most-robust!)
• radius-minimax estimator: green (optimally robust; cf. Rieder et al. (2008))

By changing the y-position of the four movable points you should recognize the instability (non-robustness) of mean and standard deviation in contrast to the robust estimates; e.g., move one of the four movable points to the top of the plot.

### Online results:

Statistics:<br>

### The underlying source code

The R script can be downloaded here.

### References

• The Costs of not Knowing the Radius, Helmut Rieder, Matthias Kohl and Peter Ruckdeschel, Statistical Methods and Application 2008 Feb; 17(1): p.13-40; cf. also [1] for an extended version.
• Robust Asymptotic Statistics, Helmut Rieder, Springer, 1994.
• Numerical Contributions to the Asymptotic Theory of Robustness, Matthias Kohl, PhD-Thesis, University of Bayreuth, 2005; cf. also [2].