# [R] Why two curves and numerical integration look so different?

C W tmrsg11 at gmail.com
Thu Feb 11 15:14:11 CET 2016

```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
>>
>> 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
>>  7.978846e+94
>> > x <- seq(-1, 4, by=0.00001) #changed -2 to -1
>> > sum(x*dnorm(x, 2, 10^(-100)))*0.00001
>>  0
>>
>> What is going here?  What a I doing wrong?
>>
>> Thanks so much!
>>
>>         [[alternative HTML version deleted]]
>>
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