Integral of PDF
You can dive into the thread "puzzle with integrate over infinite range"
from September this year. The short answer appears to be: Increase the
error tolerance.
integrate(function(x) dnorm(x, 500,50), -Inf, Inf,
subdivisions=500, rel.tol=1e-11)
# 1 with absolute error < 1.1e-12
Hans Werner
Doran, Harold wrote:
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 [[alternative HTML version deleted]]
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