I have a function F(x) = a + b / (1 + exp(-(cx + d))) and a small data set containing 5 sample: x = [10.0, 5.0, 2.0, 0.5, 0.25] and y = [23, 24, 25, 26, 27]. How can I find the suitable parameters, that is , a, b, c and d to fit this sample to the curve of the function F(x)?
Using some software I can get an answer is a = 491.5795, b = -468.6693, c = -0.3064, d = -4.7482. Suppose I already knew the value of a and b, then I can change the function F(x) to a standard logistic regression format L(x) = 1 / (1 + exp(-(cx+d))) and solve parameters c and d. So the question know is how can I find the a and b?
Finally I found the solution by myself:) 1. F(x) = a + b / (1 + exp(-(cx + d))) is a modified format of generalized logistic function, which is F(x) = A + (K-A) / (1 + exp(-B(x - M))^(1 / v) 2. Levenberg-Marquardt Rocks