[R] unimodal VS bimodal normal distribution - how to get a pvalue?

[Duncan Murdoch]

On 10/21/2008 2:56 PM, Emmanuel Levy wrote:
> Dear All,
> 
> I have a distribution of values and I would like to assess the
> uni/bimodality of the distribution.
> 
> I managed to decompose it into two normal distribs using Mclust, and
> the BIC criteria is best for two parameters.
> However, the problem is that the BIC criteria is not a P-value, which
> I would need ideally.
> 
> I saw the diptest package but it is not for gaussian distributions.
> 
> Any hint at a package or way-around this would be greatly appreciated.

If your null is really a unimodal gaussian, then doing it by simulation 
should be easy:  simulate lots of normal samples of the same size as 
your observed one, and calculate the same BIC statistic on each of them. 
  Then your p-value is the true proportion of simulated statistics that 
give stronger evidence than the observed one, and is well approximated 
by the simulated proportion.

Duncan Murdoch