R help - Aug 2015 - Simulate skewed data if 2.5, 25th 50th and 75 centile are known

Colleagues,
I need to simulate skewed data so I can run a sample size calculation.
 
I know the 2.5th, 25th, 50th, and 75th centiles of the data (32, 43, 48, 250).
 
data <- matrix(c(75,250,50,48,25,43,2.5,32),nrow=4,ncol=2,byrow=TRUE)
dimnames(data) <- list(NULL,c("x","y"))
data

Is there a way I can use these values to generate simulations of the original
data? Of course if the data were normally distributed this would be a piece of
cake, but given the skewness, I don't know how to go about the generating
the values that would be expected from a distribution having the observed values
at the four centiles.
Thank you,
John
John David Sorkin M.D., Ph.D.
Professor of Medicine
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology and Geriatric
Medicine
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing) 

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Hint: See below.

On Wednesday, August 5, 2015, John Sorkin <jsorkin at grecc.umaryland.edu>
wrote:
> Colleagues,
> I need to simulate skewed data so I can run a sample size calculation.
>
> I know the 2.5th, 25th, 50th, and 75th centiles of the data (32, 43, 48,
> 250).
>
> data <- matrix(c(75,250,50,48,25,43,2.5,32),nrow=4,ncol=2,byrow=TRUE)
> dimnames(data) <- list(NULL,c("x","y"))
> data
>
> Is there a way I can use these values to generate simulations of the
> original data? Of course if the data were normally distributed this would
> be a piece of cake,

Oh -- how? ( a normal distribution is defined by 2 parameters. You appear
to have 4. ) If you can answer this question, you can probably answer the
same question for skew data. See also things like Johnson distributions,
Pearson distributions, and other flexible distribution families. You should
also probably move to stackexchange, as this is definitely a statistical
matter. Once you decide what to do, R will have a package to do it.

Others may be able to offer better advice, so wait a bit before proceeding,
though.

-- Bert

but given the skewness, I don't know how to go about the generating
the
> values that would be expected from a distribution having the observed
> values at the four centiles.
> Thank you,
> John
> John David Sorkin M.D., Ph.D.
> Professor of Medicine
> Chief, Biostatistics and Informatics
> University of Maryland School of Medicine Division of Gerontology and
> Geriatric Medicine
> Baltimore VA Medical Center
> 10 North Greene Street
> GRECC (BT/18/GR)
> Baltimore, MD 21201-1524
> (Phone) 410-605-7119
> (Fax) 410-605-7913 (Please call phone number above prior to faxing)
>
> Confidentiality Statement:
> This email message, including any attachments, is for ...{{dropped:25}}

> On Aug 5, 2015, at 4:21 PM, Bert Gunter <bgunter.4567 at gmail.com>
wrote:
> 
> Hint: See below.
> 
> On Wednesday, August 5, 2015, John Sorkin <jsorkin at
grecc.umaryland.edu>
> wrote:
> 
>> Colleagues,
>> I need to simulate skewed data so I can run a sample size calculation.
>> 
>> I know the 2.5th, 25th, 50th, and 75th centiles of the data (32, 43,
48,
>> 250).
>> 
>> data <-
matrix(c(75,250,50,48,25,43,2.5,32),nrow=4,ncol=2,byrow=TRUE)
>> dimnames(data) <- list(NULL,c("x","y"))
>> data
>> 
>> Is there a way I can use these values to generate simulations of the
>> original data? Of course if the data were normally distributed this
would
>> be a piece of cake,
> 
> 
> Oh -- how? ( a normal distribution is defined by 2 parameters. You appear
> to have 4. ) If you can answer this question, you can probably answer the
> same question for skew data. See also things like Johnson distributions,
> Pearson distributions, and other flexible distribution families. You should
> also probably move to stackexchange, as this is definitely a statistical
> matter. Once you decide what to do, R will have a package to do it.
> 
> Others may be able to offer better advice, so wait a bit before proceeding,
> though.
> 
> -- Bert
> 
> but given the skewness, I don't know how to go about the generating the
>> values that would be expected from a distribution having the observed
>> values at the four centiles.
>> Thank you,
>> John

John,

Just to pick up on Bert?s suggestion, there are some threads over on SE that
discuss similar subject matter, one of which, due to my own curiosity, led me
to:

  https://cran.r-project.org/web/packages/rriskDistributions/index.html

which you may find of value.

Regards,

Marc Schwartz