[R] Optimization to fit data to custom density distribution
Prof Brian Ripley
ripley at stats.ox.ac.uk
Sat Mar 21 15:41:07 CET 2015
On 21/03/2015 14:27, Johannes Radinger wrote:
> Thanks for the fast response. The fitdistr() function works well for the
> predefined density functions. However, what is the recommended approach
> to optimize/fit a density function described by two superimposed normal
> distributions? In my case it is N1(mean=0,sd1)*p+N2(mean=0,sd2)*(1-p).
> With fitdistr one can only choose among the 15 distributions. Probably
That is simply not true. The help says
densfun: Either a character string or a function returning a density
evaluated at its first argument.
and the second alternative is used in the examples.
> this needs an approach using optim()? However I am so far unfamiliar
> with these packages. So any suggestion ist welcome. :)
There are examples of that in MASS (the book), chapter 16.
>
> /Johannes
>
> On Sat, Mar 21, 2015 at 2:16 PM, Prof Brian Ripley
> <ripley at stats.ox.ac.uk <mailto:ripley at stats.ox.ac.uk>> wrote:
>
> One way using the standard R distribution:
>
> library(MASS)
> ?fitdistr
>
> No optimization is needed to fit a normal distribution, though.
>
>
> On 21/03/2015 13:05, Johannes Radinger wrote:
>
> Hi,
>
> I am looking for a way to fit data (vector of values) to a
> density function
> using an optimization (ordinary least squares or maximum
> likelihood fit).
> For example if I have a vector of 100 values generated with rnorm:
>
> rnorm(n=100,mean=500,sd=50)
>
> How can I fit these data to a Gaussian density function to
> extract the mean
> and sd value of the underlying normal distribution. So the
> result should
> roughly meet the parameters of the normal distribution used to
> generate the
> data. The results will ideally be closer the true parameters the
> more data
> (n) are used to optimize the density function.
>
>
> That's a concept called 'consistency' from the statistical theory of
> estimation. If you skipped that course, time to read up (but it is
> off-topic here).
>
> --
> Brian D. Ripley, ripley at stats.ox.ac.uk <mailto:ripley at stats.ox.ac.uk>
> Emeritus Professor of Applied Statistics, University of Oxford
> 1 South Parks Road, Oxford OX1 3TG, UK
>
>
--
Brian D. Ripley, ripley at stats.ox.ac.uk
Emeritus Professor of Applied Statistics, University of Oxford
1 South Parks Road, Oxford OX1 3TG, UK
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