On Sat, Mar 21, 2015 at 3:41 PM, Prof Brian Ripley <rip...@stats.ox.ac.uk>
wrote:
> 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.
Of course, that was my mistake. So fitdistr() works fine for this case.
Here an example to complete that case:
x <- c(rnorm(mean=0,sd=50,70),rnorm(mean=0,sd=500,30))
hist(x,breaks=30)
ddoublenorm <- function(x,sigma_stat,sigma_mob,p) {
dnorm(x,mean=0,sd=sigma_stat)*p+dnorm(x,mean=0,sd=sigma_mob)*(1-p)}
fitdistr(x=x,densfun=ddoublenorm,
start=list(sigma_stat=30,sigma_mob=300,p=0.5),
method="L-BFGS-B",lower=c(0.001,0.001,0.00001),upper=c(Inf,Inf,0.99999))
Thanks a lot!
Best regards,
Johannes
>
>
> 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
>> <rip...@stats.ox.ac.uk <mailto:rip...@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, rip...@stats.ox.ac.uk <mailto:rip...@stats.ox.ac.uk>
>> Emeritus Professor of Applied Statistics, University of Oxford
>> 1 South Parks Road, Oxford OX1 3TG, UK
>>
>>
>>
>
> --
> Brian D. Ripley, rip...@stats.ox.ac.uk
> Emeritus Professor of Applied Statistics, University of Oxford
> 1 South Parks Road, Oxford OX1 3TG, UK
>
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