Complex probability distribution functions in R

General
1

Good afternoon. Could you, please, recommend me packages in R (RStudio), which can help to fit complex univariate probability distribution functions to 1 - minute logarithmic returns data? Particularly, I need:

  • generalized error distribution (GED);
  • normal inverse Gaussian distribution (NIG);
  • variance - gamma distribution (VG);
  • generalized hyperbolic distribution (GHYP);
  • Burr distribution (BURR);

Data array, on which the distribution parameters should be estimated, is rather large and includes about 30000 values.

Moreover, I`d like to know about functions or packages, which can assess, how well the chosen theoretical distribution fits the empirical distribution of data, and which can compare several theoretical probability distribution functions and choose one, that fits the given data best.

Thank you for your help.

2

Hi @Maxim,
A quick search on Google suggests that these two R packages may help:
https://cran.r-project.org/web/packages/fitdistrplus/vignettes/paper2JSS.pdf
https://cran.r-project.org/web/packages/GeneralizedHyperbolic/GeneralizedHyperbolic.pdf

Not my field, but HTH

3

Thank you for your help.

I've already tried fitdistrplus package, but it didn't help me very much.
GeneralizedHyperbolic is a bit more helpful.

5

By the way, how is it possible in R to estiamte the goodness-of-fit of the theoretical distribution to empirical data?

6

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