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I am trying to fit t-distributions to my data but am unable to do so. My first try was

fitdistr(myData, "t")

There are 41 warnings, all saying that NaNs are produced. I don't know how, logarithms seem to be involved. So I adjusted my data somewhat so that all data is >0, but I still have the same problem (9 fewer warnings though...). Same problem with sstdFit(), produces NaNs.

So instead I try with fitdist which I've seen on stackoverflow and CrossValidated:

fitdist(myData, "t")

I then get

Error in mledist(data, distname, start, fix.arg, ...) :
'start' must be defined as a named list for this distribution

What does this mean? I tried looking into the documentation but that told me nothing. I just want to possibly fit a t-distribution, this is so frustrating :P

Thanks!

Rorschach
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Erik Vesterlund
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2 Answers2

5

Start is the initial guess for the parameters of your distribution. There are logs involved because it is using maximum likelihood and hence log-likelihoods.

library(fitdistrplus)
dat <- rt(100, df=10)
fit <- fitdist(dat, "t", start=list(df=2))
Rorschach
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4

I think it's worth adding that in most cases, using the fitdistrplus package to fit a t-distribution to real data will lead to a very bad fit, which is actually quite misleading. This is because the default t-distribution functions in R are used, and they don't support shifting or scaling. That is, if your data has a mean other than 0, or is scaled in some way, then the fitdist function will simply lead to a bad fit.

In real life, if data fits a t-distribution, it is usually shifted (i.e. has a mean other than 0) and / or scaled. Let's generate some data like that:

data = 1.5*rt(10000,df=5) + 0.5

Given this data has been sampled from the t-distribution with 5 degrees of freedom, you'd think that trying to fit a t-distribution to this should work quite nicely. But actually, here is the result. It estimates a df of 2, and provides a bad fit as shown in the qq plot.

> fit_bad <- fitdist(data,"t",start=list(df=3))
> fit_bad

Fitting of the distribution ' t ' by maximum likelihood 
Parameters:
   estimate Std. Error
df 2.050967 0.04301357

> qqcomp(list(fit_bad)) # generates plot to show fit

Trying to fit a t-distribution to the data we sampled from a t-distribution with df 5 leads to a bad fit!

When you fit to a t-distribution you want to not only estimate the degrees of freedom, but also a mean and scaling parameter.

The metRology package provides a version of the t-distribution called t.scaled that has a mean and sd parameter in addition to the df parameter [metRology]. Now let's fit it again:

> library("metRology")
> fit_good <- fitdist(data,"t.scaled",
                      start=list(df=3,mean=mean(data),sd=sd(data)))
> fit_good
Fitting of the distribution ' t.scaled ' by maximum likelihood 
Parameters:
     estimate Std. Error
df   4.9732159 0.24849246
mean 0.4945922 0.01716461
sd   1.4860637 0.01828821

> qqcomp(list(fit_good)) # generates plot to show fit

Trying to fit a t-distribution to the data we sampled from a t-distribution with df 5 leads to a good fit now that we can take the mean and scaling into account

Much better :-) The parameters are very close to how we generated the data in the first place! And the QQ plot shows a much nicer fit.

Patrick
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  • The location and scale of student t in base R can be extended. https://stackoverflow.com/questions/38668587/how-to-fit-a-t-distribution-with-scale-and-location-parameters-in-fitdistrplus/60199838#60199838 – Kevin Zhu Feb 15 '20 at 02:40