1: Market

Product No. 1

No. 2

...

No. n

2: Market shares

s₁

s₂

...

s_n

3: Outside good

Select^b

4: Transformation

ln(s₁/s₀) = lshares1

Do the same as for product 1

...

5: Regression model

Mod1 = Linear Model Fit [lshares 1, t, t]

6: Regression line

d₁ + k₁ × t = Normal [Mod1]

7: Residuals normally distributed?

Anderson Darling Test [Mod 1 [“Fit Residuals”]] < 0.05?

If not: select different outside good

8: Asymptotic parameter distribution

Dist1 = Multinormal Distribution[

Mod 1 [“Best Fit Parameters”],

Mod 1 [“Covariance Matrix”]]

9: Random coefficients

{d_1r, k_1r} = Random Variate [Dist 1, 1]

10: Intermediate step

Exp_1r = Exp[d_1r + k_1r∙t]

Sum_r = Exp_1r + Exp_2r + ...

11: Simulated share

s_1r = Exp_1r/(1 + Sum_r)

s_0r = 1 − s_1r − s_2r ...