I don't see here FAQ 7.31 comes in either (for once!...) However, either the density is unnormalized and the integral is not 1, or the integral is 1 and it is normalized. The one in the picture clearly does not integrate to one. You can fit a rectangle of size 0.1 by 1e191 under the curve so the integral should be > 1e190 .
As depicted, I don't see why a plain integral from .5 to 1.5 shouldn't work. -pd On 12 Feb 2016, at 16:57 , C W <tmrs...@gmail.com> wrote: > Hi Bert, > > Yay fantasyland! > > In all seriousness, You are referring to this? > https://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f > > In particular, you mean this: .Machine$double.eps ^ 0.5? > > Thanks! > > On Fri, Feb 12, 2016 at 10:53 AM, Bert Gunter <bgunter.4...@gmail.com> > wrote: > >> You are working in fantasyland. Your density is nonsense. >> >> Please see FAQ 7.31 for links to computer precision of numeric >> calculations. >> >> >> Cheers, >> Bert >> Bert Gunter >> >> "The trouble with having an open mind is that people keep coming along >> and sticking things into it." >> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip ) >> >> >> On Fri, Feb 12, 2016 at 7:36 AM, C W <tmrs...@gmail.com> wrote: >>> Hi David, >>> >>> This is the Gaussian looking distribution I am trying to integrate. >>> >> https://drive.google.com/file/d/0B2xN0-A6iTB4NThIZ2tYdGxHc00/view?usp=sharing >>> >>> Notice the unnormalized density goes up as high as 2.5*101^191. >>> >>> I tried to create small intervals like >>>> seq(0.5, 1.3, by = 10^(-8)) >>> >>> but that doesn't seem to be good enough, as we know, it should integrate >> to >>> 1. >>> >>> On Thu, Feb 11, 2016 at 3:32 PM, David Winsemius <dwinsem...@comcast.net >>> >>> wrote: >>> >>>> >>>>> On Feb 11, 2016, at 11:30 AM, C W <tmrs...@gmail.com> wrote: >>>>> >>>>> Hi David, >>>>> >>>>> My real function is actually a multivariate normal, the simple toy 1-d >>>> normal won't work. >>>>> >>>>> But, you gave me an idea about restricting the bounds, and focus >>>> integrating on that. I will get back to you if I need any further >>>> assistance. >>>> >>>> You'll probably need to restrict your bounds even more severely than I >> did >>>> in the 1-d case (using 10 SD's on either side of the mean) . You might >> need >>>> adequate representation of points near the center of your >> hyper-rectangles. >>>> At least that's my armchair notion since I expect the densities tail off >>>> rapidly in the corners. You can shoehorn multivariate integration around >>>> the `integrate` function but it's messy and inefficient. There are other >>>> packages that would be better choices. There's an entire section on >>>> numerical differentiation and integration in CRAN Task View: Numerical >>>> Mathematics. >>>> >>>> -- >>>> David. >>>> >>>> >>>>> >>>>> Thank you so much! >>>>> >>>>> On Thu, Feb 11, 2016 at 2:06 PM, David Winsemius < >> dwinsem...@comcast.net> >>>> wrote: >>>>> >>>>>> On Feb 11, 2016, at 9:20 AM, C W <tmrs...@gmail.com> wrote: >>>>>> >>>>>> I want to do numerical integration w.r.t. mu: P(mu) × N(mu, 0.00001) >>>>>> >>>>>> Because the variance is small, it results in density like: >> 7.978846e+94 >>>>>> >>>>>> Is there any good suggestion for this? >>>>> >>>>> So what's the difficulty? It's rather like the Dirac function. >>>>> >>>>>> integrate( function(x) dnorm(x, sd=0.00001), -.0001,0.0001) >>>>> 1 with absolute error < 7.4e-05 >>>>> >>>>> >>>>> -- >>>>> David. >>>>> >>>>>> >>>>>> Thanks so much! >>>>>> >>>>>> >>>>>> On Thu, Feb 11, 2016 at 9:14 AM, C W <tmrs...@gmail.com> wrote: >>>>>> >>>>>>> Wow, thank you, that was very clear. Let me give it some more runs >>>> and >>>>>>> investigate this. >>>>>>> >>>>>>> On Thu, Feb 11, 2016 at 12:31 AM, William Dunlap < >> wdun...@tibco.com> >>>>>>> wrote: >>>>>>> >>>>>>>> Most of the mass of that distribution is within 3e-100 of 2. >>>>>>>> You have to be pretty lucky to have a point in sequence >>>>>>>> land there. (You will get at most one point there because >>>>>>>> the difference between 2 and its nearest neightbors is on >>>>>>>> the order of 1e-16.) >>>>>>>> >>>>>>>> seq(-2,4,len=101), as used by default in curve, does include 2 >>>>>>>> but seq(-3,4,len=101) and seq(-2,4,len=100) do not so >>>>>>>> curve(..., -3, 4, 101) and curve(..., -2, 4, 100) will not show >> the >>>> bump. >>>>>>>> The same principal holds for numerical integration. >>>>>>>> >>>>>>>> >>>>>>>> Bill Dunlap >>>>>>>> TIBCO Software >>>>>>>> wdunlap tibco.com >>>>>>>> >>>>>>>> On Wed, Feb 10, 2016 at 6:37 PM, C W <tmrs...@gmail.com> wrote: >>>>>>>> >>>>>>>>> Dear R, >>>>>>>>> >>>>>>>>> I am graphing the following normal density curve. Why does it >> look >>>> so >>>>>>>>> different? >>>>>>>>> >>>>>>>>> # the curves >>>>>>>>> x <- seq(-2, 4, by=0.00001) >>>>>>>>> curve(dnorm(x, 2, 10^(-100)), -4, 4) #right answer >>>>>>>>> curve(dnorm(x, 2, 10^(-100)), -3, 4) #changed -4 to -3, I get >> wrong >>>>>>>>> answer >>>>>>>>> >>>>>>>>> Why the second curve is flat? I just changed it from -4 to -3. >>>> There is >>>>>>>>> no density in that region. >>>>>>>>> >>>>>>>>> >>>>>>>>> Also, I am doing numerical integration. Why are they so >> different? >>>>>>>>> >>>>>>>>>> x <- seq(-2, 4, by=0.00001) >>>>>>>>>> sum(x*dnorm(x, 2, 10^(-100)))*0.00001 >>>>>>>>> [1] 7.978846e+94 >>>>>>>>>> x <- seq(-1, 4, by=0.00001) #changed -2 to -1 >>>>>>>>>> sum(x*dnorm(x, 2, 10^(-100)))*0.00001 >>>>>>>>> [1] 0 >>>>>>>>> >>>>>>>>> What is going here? What a I doing wrong? >>>>>>>>> >>>>>>>>> Thanks so much! >>>>>>>>> >>>>>>>>> [[alternative HTML version deleted]] >>>>>>>>> >>>>>>>>> ______________________________________________ >>>>>>>>> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, >> see >>>>>>>>> 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. >>>>>>>>> >>>>>>>> >>>>>>>> >>>>>>> >>>>>> >>>>>> [[alternative HTML version deleted]] >>>>>> >>>>>> ______________________________________________ >>>>>> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see >>>>>> 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. >>>>> >>>>> David Winsemius >>>>> Alameda, CA, USA >>>>> >>>>> >>>> >>>> David Winsemius >>>> Alameda, CA, USA >>>> >>>> >>> >>> [[alternative HTML version deleted]] >>> >>> ______________________________________________ >>> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see >>> 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. >> > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > 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. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.