[R] Simulate skewed data with known mean and median

[James Shaw]

Can anyone suggest how to simulate data from a continuous, unimodal,
positively skewed, two-tailed distribution with known mean and median
and, preferably, a known variance?  I am interested in comparing the
power of some robust estimators and wish to generate data that
resemble a known distribution with the following parameters: mean=5,
median=2, SD=9, min=-7, max=80, mode(1)=5.  I am aware of an approach
used by Thomas Hettsmansperger to evaluate his test of symmetry and am
attaching a description of the procedure.  (I believe is not against
posting rules to attach PDFs.  Sorry if I am mistaken.)
Unfortunately, this procedure yields data with a bimodal distribution,
which does not reflect the distribution of the variable I am
attempting to replicate in the simulation.  Additionally, it does not
constrain the variance of the data to take on a desired value.  I
would think that some form of contaminated normal (where observations
from the contaminating distribution take on positive values only)
would do the trick.  Any suggestions would be greatly appreciated.

-- 
Jim


Dr. James W. Shaw
134 East 56th Street
Westmont, IL 60559
Home: 630-324-6375
Mobile: 215-852-3045
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