Gompertz curve

[Marcio]

(03-30-2015 06:36 PM)salvomic Wrote:  However, about this curve I need help for the "inverse" problem: to use regression (interpolation) for that formula (Y=A*e^(-B*e^(-C*X))) with Statistic 2var (or otherwise).

I have a series of values for X (t, years) and Y (population):
X: 1,2,3,4,5,6,7,8,9
Y: 146583, 150203, 161475, 169182, 177619, 183054, 189431, 193082, 195687
I would get an estimation for A, B, C. (Then predict future values...)

I set in Symb -> Type: "User Defined" and Fit: "A*e^(-B*e^(-C*X))", but I'm not able to get plot and the values of estimated A, B, C, as I would like to have...
Any hints?

The Prime can't do that. To use customized functions, you can't put unknowns in there, meaning you have to provide values for A, B and C if you want to see data plotted against an equation. The manual discusses this a little bit.

What you could do is try to adjust the customized function to one of the options the Prime gives you. Try to make them equivalent to each other. I often do that. Quite fun.

Alternatively, if you are in a hurry or REALLY need this, I have a program that will fit data to customized functions. It's not fully integrated to the apps just yet but it will work just fine, meaning it will only work on the terminal environment. Shouldn't take more than 1 second to give the results back, provided you enter good initial values.

BTW, you will have to normalize your data before using any (or most) parameter estimation program or app.

Just like this:
Y:=Y/max(Y). That should only change the value of A, which will have to be multiplied by max(Y) after you get the results back. The values of B and C should and will not be affected by this little trick.

Marcio