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st: How to improve accuracy in numerical integrations using Stata
From
"Tiago V. Pereira" <[email protected]>
To
[email protected]
Subject
st: How to improve accuracy in numerical integrations using Stata
Date
Fri, 23 Dec 2011 14:45:27 -0200 (BRST)
Dear Maarten,
I don't have a clue on how to select specific knots, but I will
investigate that.
As usual (since 2005!) I thank you very much for you time and extremely
helpful tips!
All the best,
Tiago
---
Dear statalisters,
I am using -integ- to numerically integrate a set of functions.
An example of a function to integrate:
function_y = -2*normal((-`x'-`r'*z)/sqrt(1-`r'^2))*normalden(z)
for variable z.
In my case, the domain ranges from 0 to `x'.
So, what I am doing is the following:
*/ ------------ start example --------------
local r = 0.1
local x = 6
drop _all
range z 0 `x' 1000
generate y = -2*normal((-`x'-`r'*z)/sqrt(1-`r'^2))*normalden(z)
dydx y z, gen(yprime)
integ y z, gen(Sy)
*/ ------- end example ------------------
dis r(integral)
-5.288096*07214*e-10
to gain more precision, I have manually edited -integ- to compute values
using the double format (i.e. instead of 'gen float variable = ', it is
using 'gen double variable =').
It seems that some precision is gained:
[using the exactly same code above, but using the 'double' version, one
gets:]
dis r(integral)
-5.288096*31782*e-10
I know that the correct answer would be something like:
-5.28809630924643245856745711e-10
which is obtained from numerical integration using a C program (supposed
to be the most precise approach I am aware of).
Do you have any ideas on how to further increase the precision for
numerical integration in Stata? The problem is that I am working on heavy
tails (alpha levels below 10^-8).
All the best,
Tiago
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