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# R: st: q-q plots, theoretical distribution with values higher than the sample's cutoff point

 From "Lucia R.Latino" To Subject R: st: q-q plots, theoretical distribution with values higher than the sample's cutoff point Date Thu, 19 Jul 2012 09:39:43 +0200

```Dear Nick,

I dropped all the observations greater than 10,000 because I considered them
outliers. However, even without dropping the observations, q-q plots show
the same pattern. Also the use of the weights does not make so much
difference, as you said.

I know that the distribution is not lognormal (it is what I was trying
exactly to show),  my concern was about the plots. As I mentioned before,
the points are close enough to the 45 line degree  (in the case of the GB2
and Singh-Maddala, the points on the q-q plot fall exactly on the straight
line) till approximately the value 9,000. After that, the points depart
significantly from the 45 line degree, they become a parallel line to the
x-axis; furthermore, while the sample distribution reaches value 10,000, the
theoretical one reaches approximately value 20,000.

I think that this is a "weird" behavior of the plots or I am simply missing
something important about the q-q plots.

Best,
Lucia

-----Messaggio originale-----
Da: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Nick Cox
Inviato: mercoledì 18 luglio 2012 20:30
A: statalist@hsphsun2.harvard.edu
Oggetto: Re: st: q-q plots, theoretical distribution with values higher than
the sample's cutoff point

You have several values clumped up near 10,000. That alone does not seem
appropriate for any distribution that in principle is unbounded above. How
were these numbers calculated?

In addition, some scrutiny of your quantiles and a few quick calculations
suggest that your distribution is a fair way from lognormal. It is not
skewed or long-tailed enough given its other parameters. I haven't tried the
other distributions named, but I suspect a similar story. (I can't tell how
much difference pweights make to this, but I guess not much.)

Nick

On Wed, Jul 18, 2012 at 6:23 PM, Lucia R.Latino
<Latino@economia.uniroma2.it> wrote:
> Dear Nick,
>
> Thanks for your answer. Here you have the details of my variable. I
> hope it can be more useful to give me some feedback.
>
>  -su dec_ae, d -
> --------------------------------------------------------------------
>          Percentiles      Smallest
> |---------------------------------------|
>  1%     838.9864        11.1115
>  5%     1402.251       38.77081
> 10%     1733.309       112.4597       Obs                        11183
> 25%     2352.013       116.3163       Sum of Wgt.       11183
>
> 50%     3209.503                                Mean            3518.48
>                                      Largest           Std. Dev.
> 1648.996
> 75%      4355.16       9948.422
> 90%     5793.742       9952.207       Variance        2719189
> 95%     6790.232         9981.6       Skewness       1.017932
> 99%     8768.935       9992.487       Kurtosis       4.138746
> ------------------------------------------------------------------
>
> Thanks,
> Lucia
>
>
>
> -----Messaggio originale-----
> Da: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Nick Cox
> Inviato: mercoledì 18 luglio 2012 18:49
> A: statalist@hsphsun2.harvard.edu
> Oggetto: Re: st: q-q plots, theoretical distribution with values
> higher than the sample's cutoff point
>
> These programs are in package -qpfit- on SSC.
>
> The word "problem" here is ambiguous. My bias is to guess that your
> data don't follow any of these distributions very well and the graphs
> are telling you that. -su dec_ae, detail- would tell us a bit more.
>
> Nick
>
> On Wed, Jul 18, 2012 at 5:13 PM, Lucia Latino
> <Latino@economia.uniroma2.it>
> wrote:
>
>> I am having some problems with the q-q plots for Dagum, gb2,
>> lognormal and Singh-Maddala distributions using programs written by Nick
Cox.
>>
>> After having fit the distribution (e.g. lognfit dec_ae, svy), I run
>> the command for the q-q plot (e.g. qlogn dec_ae [pweight=iwght]).
>>
>> I repeat the same procedure for the other distributions (Dagum, gb2
>> and Singh-Maddala). All the plots show a strange behavior: in all the
>> qq-plots, the points follow a strongly nonlinear patters. At the
>> beginning they follow the 45 degree line, then they depart
>> significantly from the 45 degree line and become flat around the
>> value
> 10,000, which is the max value for dec_ae.
>>
>> What does it mean? Why the theoretical distribution takes value
>> higher than 10,000?
>>
>> I hope I was clear enough. I wish I could show you the plots, but I
>> understood I cannot attach  them.

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