[R] Fitting Distributions Directly From a Histogram

[Vincent Goulet]

Le Lundi 12 Juin 2006 06:51, Lorenzo Isella a écrit :
> Dear All,
>
> A simple question: packages like fitdistr should be ideal to analyze
> samples of data taken from a univariate distribution, but what if
> rather than the raw data of the observations you are given directly
> and only a histogram?

Let's assume that you have not only the histogram itself, but also the breaks 
and the counts per bin. Then you have what grouped data --- at least that's 
how we call those in Actuarial Science. Maximum likelyhood estimation is 
feasible for such data, but it is slightly more complicated. "Loss Models" by 
Klugman, Panjer & Willmot (Wiley) covers this.

I'm now thinking of adding this to my actuarial science package "actuar"...

> I was thinking about generating artificially a set of data
> corresponding to the counts binned in the histogram, but this sounds
> too cumbersome.
> Another question is the following: fitdistr provides the value of the
> log-likely hood function, but what if I want e.g. a chi square test to
> get some insight on the goodness of the fitting?

Goodness of fit tests for grouped data are also covered in Loss Models.

> I am sure there must be a way to get it straightforwardly without
> coding it myself.

Once you have the theory, I'm afraid for now you will have to code the 
estimation procedure yourself.

Cheers.

> Many thanks
>
> Lorenzo
>
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-- 
  Vincent Goulet, Professeur agrégé
  École d'actuariat
  Université Laval, Québec 
  Vincent.Goulet at act.ulaval.ca   http://vgoulet.act.ulaval.ca