Hi,
You need to be careful with -Inf and Inf in R, I suppose they are some large
numbers arbitrarily chosen by R, but not infinite quantities. So the function
integrate can return errors if the function to integrate doesn't have
negligible values beyond those large numbers.
I ran the following to convince myself:
> integrate(function(x){return(ifelse(x<500,0,1/(x^2)))},-Inf,Inf)
0 with absolute error < 0
> integrate(function(x){return(ifelse(x<500,0,1/(x^2)))},500,Inf)
0.001999999 with absolute error < 0.000011
The second result shouldn't be greater that the first one but...
And to solve your problem:
> integrate(function(x) dnorm(x, 500,50), 500-1000, 500+1000)
1 with absolute error < 0.000074
I centred the interval of integration on 500 instead of on 0 if you integrate
between -Inf and Inf.
HTH,
Samuel
-----Original Message-----
From: [email protected] [mailto:[email protected]] On
Behalf Of Doran, Harold
Sent: 02 December 2010 21:22
To: [email protected]
Subject: [R] Integral of PDF
The integral of any probability density from -Inf to Inf should equal 1,
correct? I don't understand last result below.
> integrate(function(x) dnorm(x, 0,1), -Inf, Inf)
1 with absolute error < 9.4e-05
> integrate(function(x) dnorm(x, 100,10), -Inf, Inf)
1 with absolute error < 0.00012
> integrate(function(x) dnorm(x, 500,50), -Inf, Inf)
8.410947e-11 with absolute error < 1.6e-10
> all.equal(integrate(function(x) dnorm(x, 500,50), -Inf, Inf)$value, 0)
[1] TRUE
> sessionInfo()
R version 2.10.1 (2009-12-14)
i386-pc-mingw32
locale:
[1] LC_COLLATE=English_United States.1252 LC_CTYPE=English_United States.1252
[3] LC_MONETARY=English_United States.1252 LC_NUMERIC=C
[5] LC_TIME=English_United States.1252
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] statmod_1.4.6 mlmRev_0.99875-1 lme4_0.999375-35 Matrix_0.999375-33
lattice_0.17-26
loaded via a namespace (and not attached):
[1] grid_2.10.1 nlme_3.1-96 stats4_2.10.1 tools_2.10.1
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