Just a correction: if we take X+2a then everything is OK (the curves intersect at a), so a = 0.9345893 is correct but one must take X ~ N(0,1) and Y ~N(2*a,1).
--- On Tue, 9/9/08, Moshe Olshansky <[EMAIL PROTECTED]> wrote: > From: Moshe Olshansky <[EMAIL PROTECTED]> > Subject: Re: [R] densities with overlapping area of 0.35 > To: r-help@r-project.org, "Lavan" <[EMAIL PROTECTED]> > Received: Tuesday, 9 September, 2008, 12:37 PM > Let X be normally distributed with mean 0 and let f be > it's density. Now the density of X+a will be f shifted > right by a. Since the density is symmetric around mean it > follows that the area of overlap of the two densities is > exactly P(X>a) + P(X<-a). > So if X~N(0,1), we want P(X>a) + P(X<-a) = > 2P(X<-a) = 0.35, so P(X<-a) = 0.175 which yields -a = > qnorm(0.175) = -0.9345893, so a = 0.9345893. > > > --- On Tue, 9/9/08, Lavan <[EMAIL PROTECTED]> > wrote: > > > From: Lavan <[EMAIL PROTECTED]> > > Subject: [R] densities with overlapping area of 0.35 > > To: r-help@r-project.org > > Received: Tuesday, 9 September, 2008, 12:11 PM > > Hi, > > > > I like to generate two normal densities such that the > > overlapping area > > between them is 0.35. Is there any code/package > available > > in R to do that?? > > > > Regards, > > > > Lavan > > -- > > View this message in context: > > > http://www.nabble.com/densities-with-overlapping-area-of-0.35-tp19384741p19384741.html > > Sent from the R help mailing list archive at > Nabble.com. > > > > ______________________________________________ > > 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. > > ______________________________________________ > 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. ______________________________________________ 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.
