In my research work, I want to do the vehicle survival fraction; survival rates were calculated using the log-logistic survival function. In equation two unknown parameters a, and b are obtained by minimising the sum of squared errors between the experimental and modelled. The equation of the model is:

S = [1 + (t/a)^b]^(-1)

age of the vehicle t = [0;1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20];

registered vehicles of respective age t, N = [6801342;6364669;6104616;5849372;5426898;4969076;4549439;4117610;3714272;3324896;2980512;2652830;2320935;2041282;1818527;1594733;1335572;1053197;800212;566590;376620];

experimental value u_exp = [406183941.2;270789294.1;812367882.4;541578588.2;406183941.2;1353946471;406183941.2;135394647.1;135394647.1;135394647.1;676973235.3;270789294.1;406183941.2;0;270789294.1;406183941.2;0;135394647.1;0;0;135394647.1];

u_mod = ((1+(t./a).^a).^(-1))*N; (modeled value = S*N)

and I want to calculate the parameters “a” and “b” by minimizing the sum of squared errors between “n exp” and “n model”.

Someone here can help me by writing the Matlab code, please?

Thank you already for your help!