HI

[anvar]

Dear Ulrich Eckhardt and Jean-Michel Pichavant!

First of all thank you for your attention. I'have never expected to
receive response.

Actually, I am doing my internship in Marketing Division in small
company., I got this assignment yesterday morning. My boss wants
perfect technology diffusion based forecasting model. I found the
required model, modified it..but cannot solve it (university friend
suggested Python because it had special tools for optimization). I
will appreciate if you help me to find right tools and give some more
advises.

Thank you for your precious time.

As to problem, I should use nonlinear least-square estimation
methodology (to estimate p_i, q_i, and β parameters) where the
objective of the estimation procedure is minimization of the sum of
squared error. Here in problem:
F_i (t)	the cumulative density function at time t for technology
generation i
f_i (t)	the probability density function at time t for technology
generation i
p_i	the proportion of mass media communication for generation i
q_i	the proportion of word of mouth for generation i
μ_i (t)	the market share at time t for generation i  (data exists)
M_i	total market potential for generation i,   (data exists)
S_i	total sales potential for generation i, S_i=μ_i (t)M_i
τ_i	the introduction time for generation i, τ_i≥1      (data exists)
s_i (t)	the actual sales of products at time t for generation
i              (data exists)
s ̂_i (t) the estimated sales of products at time t for generation i
X_i (t)	the cumulative market effects
β	the effectiveness of the price
〖pr〗_i (t)	the price at time t for generation i          (data exists)
α_t	the seasonal factor at time t             (data exists)
g_t	the growth rate at time t           (data exists)
n	the number of generations             (data exists)
l	the number of periods              (data exists)
C_i (t)	the capacity restriction regarding the product at time t for
generation i             (data exists)