Dear Nick,Stephen,fellows !
I think deconvolution works for a simple example of two lognormal components
using modified Simpson for integration:
I type:
clear
set obs 4
input y
1
0
0
0
then I type >do simpson<
~~~
capture program drop nlfaq
program nlfaq
if "`1'" == "?" {
global S_1 " m1 m2 sigma1 sigma2 "
global m1 = 1
global m2 = 1
global sigma1 = 1
global sigma2 = 1
exit
}
tempvar yh
* global sigma1=1
*egen `X' = (_n<=34)*sum(_n*cos($B) + _n-1*tan($B))
#delimit;
gen `yh' =(0.4/12)* ((1/sqrt(2*_pi))*(1/$sigma1)*(1/.1)* exp(-(log(.51 - .1)
- $m1 )^2/2*($sigma1^2)) * (1/sqrt(2*_pi))*(1/$sigma2)*(1/.1)* exp(-(log(.1)
- $m2)^2/2*($sigma2^2))
+ 4*(1/sqrt(2*_pi))*(1/$sigma1)*(1/.2)* exp(-(log(.51 - .2) -
$m1 )^2/2*($sigma1^2)) * (1/sqrt(2*_pi))*(1/$sigma2)*(1/.2)* exp(-(log(.2) -
$m2)^2/2*($sigma2^2))
+ 2*(1/sqrt(2*_pi))*(1/$sigma1)*(1/.3)* exp(-(log(.51 - .3) -
$m1 )^2/2*($sigma1^2)) * (1/sqrt(2*_pi))*(1/$sigma2)*(1/.3)* exp(-(log(.3) -
$m2)^2/2*($sigma2^2))
+ 4*(1/sqrt(2*_pi))*(1/$sigma1)*(1/.4)* exp(-(log(.51 - .4) -
$m1 )^2/2*($sigma1^2)) * (1/sqrt(2*_pi))*(1/$sigma2)*(1/.4)* exp(-(log(.4) -
$m2)^2/2*($sigma2^2))
+ (1/sqrt(2*_pi))*(1/$sigma1)*(1/.4)* exp(-(log(.51 - .5) - $m1
)^2/2*($sigma1^2)) * (1/sqrt(2*_pi))*(1/$sigma2)*(1/.4)* exp(-(log(.4) -
$m2)^2/2*($sigma2^2))) in 1;
#delimit cr
* gen `yh'= exp($A) + `X' - 2 in 1
replace `yh'= $sigma1 - $sigma2 in 2
replace `yh'= $m1 - $m2 in 3
replace `yh'= $m1 - $sigma2 in 4
replace `1' = `yh'
end
nl faq y
di $sigma1,$sigma2
di $m1,$m2
di $m1,$sigma2
I'd like to be successful for a great number of Simpson steps.
I could not bring egen-idea to work.
/Simpson rule: (b-a)/3n*{ya + 4y1+2y2 .. +2y(n-2)+4y(n-1) + yb} as integral
from a to b /
thanks to all
aa
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