I wouldn't go quite so far as to say there's absolutely nothing else -- one could, e.g., also fit lognormal, gamma, beta or most any other two parameters distributions from the supplied data [assuming the support matches].
What I did say is that you need domain specific knowledge to pick a distribution to which to fit: then, if the moments are known in closed form from the parameters, moment matching comes down to simultaneous non-linear equations. I'm not aware of a unified infrastructure for this in R [so I'm cc'ing the list in case someone else is], but it's not a terribly difficult problem for the low dimensions we're talking about. E.g., If you know your data has a gamma distribution with mean 10 and variance 20, you look at the Wikipedia gamma distribution page to find Mean = k * theta Variance = k * theta * theta So Variance / Mean = theta --> Theta = 2 for your problem. Then k = 5. Similarly, the all-great Wikipedians provide closed form solutions to get the lognormal parameters back from observed sample moments: http://en.wikipedia.org/wiki/Lognormal_distribution#Arithmetic_moments As Bert rightly cautions, this is far outside the realm of good practice and your energies would be better served if you could get a better picture of the underlying data. Best, Michael On Fri, Jun 8, 2012 at 9:13 AM, Bert Gunter <gunter.ber...@gene.com> wrote: > > Andras: > I realize my comment was rather cryptic, but which part of Michael's "You > can't" did you not understand? Other then > > ?dnorm > > which, as Michael said, is probably not a good thing, you can do nothing. You > need to refocus your efforts on changing the system to get useful data, not > trying to make a silk purse out of a sow's ear. Or, as John Tukey said many > years ago: > > "The combination of some data and an aching desire for an answer does not > ensure that a reasonable answer can be extracted from a given body of data. " > -- John Tukey > > -- Bert > > > > > On Fri, Jun 8, 2012 at 5:14 AM, Andras Farkas <motyoc...@yahoo.com> wrote: >> >> >> Dear Bert and Michael >> >> thank you for your note below. Based on Michael's input and the lack of >> covariance matrix availble to me (for the most part), moment matching sounds >> like the best option. I have searched the internet for discussions on this >> using R but did not find much useful information. I also have to apologize, >> but I am somewhat new to the software and this level of statistics.I am >> usually pretty good at figuring things out, but this one is probably way >> over my head. I was wondering if you could point me into the right direction >> using R to "re-build" the distribution that has the following parameters: >> >> mean: 0.007, median: 0.003, SD:0.011. >> >> I greatly apreciate your help, >> >> Sincerely, >> >> Andras >> >> gunter.ber...@gene.com> wrote: >> >> >> From: Bert Gunter <gunter.ber...@gene.com> >> Subject: Re: [R] "Re-creating" distributions >> To: "R. Michael Weylandt" <michael.weyla...@gmail.com> >> Cc: "Andras Farkas" <motyoc...@yahoo.com>, r-help@r-project.org >> Date: Friday, June 8, 2012, 12:29 AM >> >> Related comment: >> >> "Even the data aren't sufficient." -- Brian Joiner (some years ago). >> >> Explanation: See W.E. Deming on "analytic" vs "enumerative" statistics. >> >> --- Bert >> >> On Thu, Jun 7, 2012 at 8:06 PM, R. Michael Weylandt >> <michael.weyla...@gmail.com> wrote: >> > Short answer: no, those are (in general) insufficient parameters to >> > characterize a distribution. >> > >> > Long answer: unfortunately, it's not uncommon that those "summary >> > statistics" are the only ones reported based on someone or other's >> > limited experience with the Gaussian. There are a few things you could >> > try, but each of them has problems: >> > >> > i) Pretend like your data is in fact normal and use those parameters >> > because they do uniquely characterize a normal distribution. MASS >> > (among others) provides a multivariate normal distribution [mvrnorm] >> > if you have a covariance matrix available. >> > >> > ii) If you have reason to imagine another distribution [guided by >> > domain knowledge], try to get its parameters in so far as possible by >> > moment matching. Covariance structures are much harder for the general >> > case though. >> > >> > iii) If you can get something that resembles original data, simply >> > work by bootstrapping / imputation. >> > >> > Hope this helps, >> > Michael >> > >> > On Thu, Jun 7, 2012 at 3:34 PM, Andras Farkas <motyoc...@yahoo.com> wrote: >> >> Dear All, >> >> >> >> I often have to work with certain models in which I try to "reproduce" a >> >> distribution the best I can with very little known information avaible. >> >> Is there a package or function in R that could best reproduce a >> >> probability distribution using only the mean, median and SD values >> >> availble without knowing the actual distribution type to begin with >> >> and/or the covariance matrix (for more then 1 data set)? All I usually >> >> have reported availble is mean, median and SD. I hope I made my >> >> question clear enough... >> >> >> >> thanks, >> >> >> >> Andras >> >> >> >> ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
