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]]
William Dunlap
2016-Feb-11 05:31 UTC
[R] Why two curves and numerical integration look so different?
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 <tmrsg11 at 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 at 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]]
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 <wdunlap at 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 <tmrsg11 at 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 at 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]]