Analyze data with the Statistics software R
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!)
- optimally robust radius-minimax estimator: green (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.
The underlying source code
The R script can be downloaded here.
- 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  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 .