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


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: q-q plots, theoretical distribution with values higher than the sample's cutoff point
Date   Wed, 18 Jul 2012 19:29:32 +0100

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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