RE: st: Estimate 95th percentile of a highly skewed distribution from summary stats?

["Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>]

Jordan - Using only the information you have given, here's three possible distributions assuming yours is a mixture of a mass at zero with probability PZ, and a gamma(la, al) with probability 1- PZ. Since the median is still zero and the 75th percentile is 7, this bonds PZ between .50 and 0.75. As you can see, using this model produces values of the 95th percentile between 9.01 and 13.6


P(zero)    alpha     lamda      mean       75th      95th 
.74       2.3958     8.0270     5.0000     7.0005    13.6025
.60       2.4631     5.0750     5.0000     7.0003     9.7534
.51       1.7765     5.7440     5.0000     7.0001     9.0110


p.s. This was fun!

Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Jordan Silberman
Sent: Wednesday, August 07, 2013 10:58 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Estimate 95th percentile of a highly skewed distribution from summary stats?

Thank you Nick. Yes, unfortunately I know nothing about the distribution other than what I posted, so a simple summarize command won't work. Jordan

On Wed, Aug 7, 2013 at 7:42 AM, Nick Cox <njcoxstata@gmail.com> wrote:
> Evidently the point of this is that _you know nothing except what you 
> have shown us_.
>
> Otherwise -summarize, detail- would do this for you, without even 
> needing to look up the more specialised commands it cross-references.
>
> The flip answer is somewhere in [7, 50]. I don't know how to improve 
> on that flip answer without making very strong assumptions about the 
> distribution. You don't even know what the fraction of zeros is.
>
> If this were my problem I would use the maximum, knowing that it is biased.
> Nick
> njcoxstata@gmail.com
>
>
> On 7 August 2013 12:23, Jordan Silberman <silberman.stata@gmail.com> wrote:
>> Hi Stata folks,
>>
>> I have some (but not all) descriptive stats for a highly skewed, 
>> zero-inflated distribution. I need to estimate the 95th percentile 
>> score for this distribution.
>>
>> Here's the info I have:
>>
>> min value: 0
>> max: 50
>> mean: 5
>> median: 0
>> 75th percentile: 7
>>
>> Obviously the distribution is highly skewed to the right. Does anyone 
>> know of a method through which I can estimate the 95th percentile 
>> score for this distribution?
>>
>> The background is that this is a distribution of estimation errors 
>> for an algorithm, and I need an estimate of a value that the error is 
>> equal to or less than in 95% of cases.
>>
>> Thanks,
>> Jordan
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/faqs/resources/statalist-faq/
>> *   http://www.ats.ucla.edu/stat/stata/
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/faqs/resources/statalist-faq/
> *   http://www.ats.ucla.edu/stat/stata/
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/