R help - Jul 2020 - Testing wether my dataset follows a poisson distribution with R

Dear friends,

I have a sample dataset, which is basically the number of transits through
a particular waterway, and is on a daily basis.

MyDat <- dataset$DailyTransits

What I?d like to do is to test whether MyDat follows a poisson distribution
or not. What R function could accomplish this?

Any help and/or guidance will be greatly appreciated,

Best regards,

Paul

	[[alternative HTML version deleted]]

Your first check might be to see in the mean and sd are "reasonably" 
close. Next approach would be to see if the `qqplot` of that vector has 
an arguably straight-line relationship with a random draw from a Poisson 
random generator function with the same mean.

?rpois

?qqplot

And do remember that Rhelp is a plain-text mailing list.

-- 

David

On 7/21/20 7:26 PM, Paul Bernal wrote:
> Dear friends,
>
> I have a sample dataset, which is basically the number of transits through
> a particular waterway, and is on a daily basis.
>
> MyDat <- dataset$DailyTransits
>
> What I?d like to do is to test whether MyDat follows a poisson distribution
> or not. What R function could accomplish this?
>
> Any help and/or guidance will be greatly appreciated,
>
> Best regards,
>
> Paul
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

That is logically impossible.

You can only show that there is insufficient evidence (according to
whatever evidentiary criterion you have chosen) to show that the data were
*not* a (iid or other) sample from a Poisson. This may seem esoteric, but
it is not. (The simplest incantation is that you can reject, but not accept
a hypothesis in the classical N-P frequentist framework ). Given sufficient
data, you will almost always have enough evidence to be formally
inconsistent with any prechosen model/distribution. This does not mean that
the model is not useful, however.

Further discussion would meander even farther offtopic. These are
statistical (and philosophy of science) issues that don't properly belong
here. Mea culpa.

Bert Gunter

"The trouble with having an open mind is that people keep coming along and
sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Tue, Jul 21, 2020 at 7:27 PM Paul Bernal <paulbernal07 at gmail.com>
wrote:
> Dear friends,
>
> I have a sample dataset, which is basically the number of transits through
> a particular waterway, and is on a daily basis.
>
> MyDat <- dataset$DailyTransits
>
> What I?d like to do is to test whether MyDat follows a poisson distribution
> or not. What R function could accomplish this?
>
> Any help and/or guidance will be greatly appreciated,
>
> Best regards,
>
> Paul
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
	[[alternative HTML version deleted]]

On 22/07/20 2:26 pm, Paul Bernal wrote:
> Dear friends,
> 
> I have a sample dataset, which is basically the number of transits through
> a particular waterway, and is on a daily basis.
> 
> MyDat <- dataset$DailyTransits
> 
> What I?d like to do is to test whether MyDat follows a poisson distribution
> or not. What R function could accomplish this?
> 
> Any help and/or guidance will be greatly appreciated,
I presume (your question is a bit vague) that you want to do a goodness 
of fit test of the Poisson distribution to your data.  Doing such a test 
would, I think, involve the assumption that your observations are 
independent and identically distributed (i.i.d.).  Since you appear to 
have a time series of daily counts, this assumption is unlikely to be valid.

Modelling such a time series and investigating whether the underlying 
marginal distributions are Poisson is likely to be a fairly subtle 
problem.  Others may be able to offer more insight here.  However such a 
discussion would be about statistical theory and methodology and  hence 
inappropriate for this list.

If you make the (likely to be untenable) assumption that your data are 
i.i.d. then such a g.o.f. test is probably most appropriately done using 
a chi-squared goodness of fit test.

The function chisq.test() would  help you.  Getting the details right 
may prove a bit tricky, but if you can't handle that, then you should 
probably seek "local" statistical advice.

In fact, you should (in view of the likely lack of independence of your 
data) seek local statistical advice in any case.

cheers,

Rolf Turner

P.S. Please note that it's "whether" not "wether".  (A
wether is a
castrated ram.)  Also "Poisson" should be capitalised.  (It's a
bloke's
name.)

R. T.

-- 
Honorary Research Fellow
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276