[R] Simulate skewed data if 2.5, 25th 50th and 75 centile are known

[Marc Schwartz]

> 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