RMA biomodality, distribution and transformation
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Benjamin Otto ▴ 830
@benjamin-otto-1519
Last seen 8.2 years ago
Dear bioconductors, some time ago in one of the discussion about RMA-bimodality Wolfgang Huber and Peter Warren pointed out, that a similar distribution could be simulated with > n <- 10000 > z = 20 + exp(c(rnorm(n), 3+rnorm(n))) > plot(density(log2(z))) Now here comes a more mathematical question. Suppose the following > x0 <- rnorm(n) > x1 <- x0 + 3 It is quite easy to get the same density in two ways: for x0 it's super easy: > plot(density(x0)) > plot(x0,dnorm(x0)) and for x1 it's still intuitive: > plot(density(x1)) > plot(x1,dnorm(x1 - 3)) That's because we are currently only shifting the distribution. But how do I transform the x-values for y-value calculation via dnorm() when applying the more complex exponential function? > x2 <- exp(x0) > plot(density(x2)) > plot(x2, ..???..) best regards Benjamin -- Pflichtangaben gem?? Gesetz ?ber elektronische Handelsregister und Genossenschaftsregister sowie das Unternehmensregister (EHUG): Universit?tsklinikum Hamburg-Eppendorf K?rperschaft des ?ffentlichen Rechts Gerichtsstand: Hamburg Vorstandsmitglieder: Prof. Dr. J?rg F. Debatin (Vorsitzender) Dr. Alexander Kirstein Ricarda Klein Prof. Dr. Dr. Uwe Koch-Gromus
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Claus Mayer ▴ 340
@claus-mayer-1179
Last seen 8.2 years ago
European Union
Dear Benjamin, what you are looking for seems to be, what is called the "The Change of Variables Formula" in English (or the "Dichtetransformationssatz" in German). Google gave me the following page as one of the first few hits: http://www.math.uah.edu/stat/dist/Transformations.xhtml Any text book on the basics of probability theory should cover that too. Hope this helps claus Benjamin Otto wrote: > Dear bioconductors, > > some time ago in one of the discussion about RMA-bimodality Wolfgang > Huber and Peter Warren pointed out, that a similar distribution could be > simulated with > > >> n <- 10000 >> z = 20 + exp(c(rnorm(n), 3+rnorm(n))) >> plot(density(log2(z))) >> > > Now here comes a more mathematical question. Suppose the following > > >> x0 <- rnorm(n) >> x1 <- x0 + 3 >> > > It is quite easy to get the same density in two ways: > > for x0 it's super easy: > >> plot(density(x0)) >> plot(x0,dnorm(x0)) >> > > and for x1 it's still intuitive: > >> plot(density(x1)) >> plot(x1,dnorm(x1 - 3)) >> > > That's because we are currently only shifting the distribution. But how > do I transform the x-values for y-value calculation via dnorm() when > applying the more complex exponential function? > > >> x2 <- exp(x0) >> plot(density(x2)) >> plot(x2, ..???..) >> > > best regards > > Benjamin > > > > > > -------------------------------------------------------------------- ---- > > _______________________________________________ > Bioconductor mailing list > Bioconductor at stat.math.ethz.ch > https://stat.ethz.ch/mailman/listinfo/bioconductor > Search the archives: http://news.gmane.org/gmane.science.biology.informatics.conductor > -------------------------------------------------------------------- ---- > > > > > > Click link below to report this email as spam. > https://www.mailcontrol.com/sr/dXJpYLPTnQPcohtw78djyckOPAo3QOzY+a8Hb o5Ixx2GVTeMoxBhVj5NdmcjVRAn3RwZV56Ny2NfAchUXJwv+Q== > -- ********************************************************************** ************* Dr Claus-D. Mayer | http://www.bioss.ac.uk Biomathematics & Statistics Scotland | email: claus at bioss.ac.uk Rowett Research Institute | Telephone: +44 (0) 1224 716652 Aberdeen AB21 9SB, Scotland, UK. | Fax: +44 (0) 1224 715349
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