# [R] Summary on random data with zero skew and some kurtosis

Abdul Kudus akudus at stat.unisba.ac.id
Thu Oct 4 03:13:45 CEST 2001

```Thanks to all who response my problem.  Here are my summary :

1.  from Dirk Eddelbuettel <edd at debian.org>

We could try a mixture of normals -- ie flip a coin (use a uniform with
some cutoff c where 0 < c < 1 ) to choose between N(0, sigma_1) and N(0,
sigma_2).

2.  from Michaell Taylor <michaell.taylor at reis.com>

We could use the gld library to specify the lambdas of virtually any
distribution, including the one that you are interested in.  It is
available  from CRAN.

Calculating the lambda's from known moments is a bit tricker, but he
has a Maple routine to do just that.

3.  from Uwe Ligges <ligges at statistik.uni-dortmund.de>

That's a theoretical problem, not an R problem. Or I misunderstood....

At first select a distribution, which
a) has zero skewness
b) a well defined and preferably easy to calculate kurtosis.

After that, choose the parameters of the distribution, so that the
theoretical value of the kurtosis is equal to the value you want to
get.

At last generate renadom numbers for that distribution with the now
given parameters.

4.  from John Fox <jfox at mcmaster.ca>

Why not sample from a t-distribution with small df?

5.  Thomas Lumley <tlumley at u.washington.edu>

The t-distribution family may help.  These have zero skewness and
kurtosis ranging from the normal to infinite. He doen't know offhand the
relationship between degrees of freedom and kurtosis, but it should be
easy to look up (or evaluate by simulation).

6.  Bob Wheeler <bwheeler at echip.com>

We can use the Johnson system. See the SuppDists package.

Abdul Kudus
=====================
Dept. of Statistics
Bandung Islamic University
Indonesia
====================

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```