[R] Random Nos

Prof Brian Ripley ripley at stats.ox.ac.uk
Sat Feb 3 22:03:32 CET 2001

On 3 Feb 2001, Saptarshi The Dude Guha wrote:

> R-lings,
> I know the algo for Laplace generation, but arent there any packages available.

It's one line in R!  Or at least, one algorithm is, for there are many.

> Also, i'm trying to check for the Bernoulli sums obey the CLT, but though i calculate 2000 values of
>            S(n)-n*p
>           ----------
>            sqrt(n*p*(1-p))
> for p=.5 and n=45, this fails both KS test and shapiro test.
> Why??

Maybe because the CLT is a limit for large n?  Or maybe you did not use
the correct distribution theory for those tests?  That for the KS test
applies to samples from a continuous distribution, and yours is quite
discrete.  I'll leave you to look this up.  The rate of divergence from
the CLT is known almost exactly in this case, and I suspect that the
distribution of the Smirnov statistic is too.

At its simplest, if you take a large enough sample you will reject
any null hypothesis outside the realm of theory.  Even if you had
generated using rnorm() in R, the distribution is slightly non-normal
(and slightly non-independent between samples).

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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