- #1
Rajini
- 621
- 4
Hello all,
I have a data which look like reversed exponentially modified Gaussian (EMG) function and interested to fit the data with with reversed EMG function. After searching on internet I found the EMG function, which is given below:
##y=\frac{ac\sqrt{2\pi}}{2d}\rm{exp}[\frac{c^2}{2d^2}-\frac{x-b}{d}][\frac{d}{|d|}+\rm{erf}(\frac{x-b}{c\sqrt2}-\frac{c}{d\sqrt2})]##
gnuplot code
Here a=Gaussian height, b=Gaussian position, c=Gaussian width, d=time constant.
When I plot the above function in gnuplot I get a curve shown in fig1.
Now I reversed the EMG so the function becomes as below (just changed the signs):
##y=\frac{ac\sqrt{2\pi}}{2d}\rm{exp}[\frac{c^2}{2d^2}+\frac{x-b}{d}][\frac{d}{|d|}-\rm{erf}(\frac{x-b}{c\sqrt2}-\frac{c}{d\sqrt2})]## and the curve is shown in fig2.
gnuplot code
For the above two EMGs I used a=2, b=30, c=1, and d=3.
1. My doubt is why both curves has different height (height a)? or I did anything wrong? Is 'a' really height?
2. I took 'a' as 2. But the height is 0.9 for EMG (fig1) and 1.13 for reversed EMG (in fig2).
Any insights will be helpful.
Thanks for your reply
Cheers,
Rajini
I have a data which look like reversed exponentially modified Gaussian (EMG) function and interested to fit the data with with reversed EMG function. After searching on internet I found the EMG function, which is given below:
##y=\frac{ac\sqrt{2\pi}}{2d}\rm{exp}[\frac{c^2}{2d^2}-\frac{x-b}{d}][\frac{d}{|d|}+\rm{erf}(\frac{x-b}{c\sqrt2}-\frac{c}{d\sqrt2})]##
gnuplot code
PHP:
f(x)=(((a*c*sqrt(2*pi))/(2*d))*exp(((c*c)/(2*d*d))-((x-b)/d))*((d/(abs(d)))+erf(((x-b)/(c*sqrt(2)))-(c/(d*sqrt(2))))))
When I plot the above function in gnuplot I get a curve shown in fig1.
Now I reversed the EMG so the function becomes as below (just changed the signs):
##y=\frac{ac\sqrt{2\pi}}{2d}\rm{exp}[\frac{c^2}{2d^2}+\frac{x-b}{d}][\frac{d}{|d|}-\rm{erf}(\frac{x-b}{c\sqrt2}-\frac{c}{d\sqrt2})]## and the curve is shown in fig2.
gnuplot code
PHP:
f(x)=(((a*c*sqrt(2*pi))/(2*d))*exp(((c*c)/(2*d*d))+((x-b)/d))*((d/(abs(d)))-erf(((x-b)/(c*sqrt(2)))-(c/(d*sqrt(2))))))
1. My doubt is why both curves has different height (height a)? or I did anything wrong? Is 'a' really height?
2. I took 'a' as 2. But the height is 0.9 for EMG (fig1) and 1.13 for reversed EMG (in fig2).
Any insights will be helpful.
Thanks for your reply
Cheers,
Rajini