R help - Mar 2015 - Optimization to fit data to custom density distribution

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 this
needs an approach using optim()? However I am so far unfamiliar with these
packages. So any suggestion ist welcome. :)

/Johannes

On Sat, Mar 21, 2015 at 2:16 PM, Prof Brian Ripley <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
> Emeritus Professor of Applied Statistics, University of Oxford
> 1 South Parks Road, Oxford OX1 3TG, UK
>
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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

On Sat, Mar 21, 2015 at 3:41 PM, Prof Brian Ripley <ripley at
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
>> <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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