how to solve the modified gompertz equation

Hi guys, I have a set of data y and t, which is given below:

y=[10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35 37.5 40 42.5 45 47.5 50];
 t=[62.1 77.3 92.5 104 112.9 121.9 125 129.4 134 138.2 142.3 143.2 144.6 147.2 147.8 149.1 150.9];

I'd like to have a curve fitting like ? = ? ??? (−???[((?*?)/?)(? −t)+1] and determine the constants of this equation (A,? and ?) . I am wandering if someone could help me with this. Thanks

[Star Strider]

What is e?

[nawalul azka]

e is euler number, e = 2.7182

Answer 1

[Star Strider]

Try this:

y=[10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35 37.5 40 42.5 45 47.5 50]; 
t=[62.1 77.3 92.5 104 112.9 121.9 125 129.4 134 138.2 142.3 143.2 144.6 147.2 147.8 149.1 150.9];

% % b(1) = A,  B(2) = mu,  b(3) = lambda
mgompertz = @(b,t) b(1) .* exp(-exp((b(2) .* exp(1))./b(1)) .* (b(3)-t) + 1);

[B,resnorm] = fminsearch(@(b) norm(y - mgompertz(b,t)), [1.4; -0.7; 37; 7])

figure
plot(t, y, 'p')
hold on
plot(t, mgompertz(B,t), '-r')
grid on

B =
         0.719308092777122
         -1.01103662495143
          6.51690967061002

resnorm =
           9.2295112377694

The plot appears to provide a decent fit.

EDIT — Eliminated ‘b(4)’, replaced it with ‘exp(1)’.

[nawalul azka]

thank you very much for your helped. this is so meaningful for me.

[Star Strider]

As always, my pleasure.

[Alex Backer]

Star Strider,

would you kindly provide a form of this function that works more generally to find the parameters of a Gompertz function given a timeline?

Specifically, what should [1.4; -0.7; 37; 7] and b1, b2, and b3 replaced with?

Thanks!

[Mattana Pongsopon]

Alex Backer,

Have you found the solution to your question about what should [1.4; -0.7; 37; 7] and b1, b2, and b3 replaced with? Because I'm also looking for the same.

Thank you :)

[Star Strider]

The ‘b’ vector, ‘b(1)’ and the others, are parameters of the ‘mgompertz’ equation, and are estimated in the fminsearch call. The ‘[1.4; -0.7; 37; 7]’ vector are the initial estimates for the parameters, necessary when doing nonlinear parameter estimation. (There only need to be three of them, since the function only has three parameters. I did not catch that when I posted my code. The function only uses the first three.)

The code I posted is as general as it gets for the version of the Gompertz equation in the Question. Other versions of the Gompertz equation would require different versions of the function.

[Mattana Pongsopon]

Star Strider,

Thank you so much for your response. It's of much help :)

[Star Strider]

My pleasure!