# How to model market share or a fraction of anything that sums to 100%?

Suppose we have sales of 3 products A, B and C which market share always sum up to 100%. How to model market share of product A using market shares of B and C? So that we will know that if share of A grows 1 percentage point then A has to steal that growth in some proportion form products B and C.

A means increase of share = A on Tuesday - A on Monday, and so on with B, C.

A = 0*A + b1*B + c1*C
B = a2*A + 0*B + c2*C
C = a3*A + b3*B + 0*C
b1+c1=-1
a2+c2=-1
a3+b3=-1


How to estimate it? Is there any other method how to estimate structure which sums to 100% by the parts of the structure? Regression doesn't work here.

• It seems you've made an edit without being logged in, thus it is showed as an anonymous one. Next time, please check it out before sending -- this way it will be applied right away. – user88 Jul 7 '12 at 21:37
• To alternatives I can think of, 1) estimate a model for the sales of A,B,C and calculate the shares afterward. 2) estimate a model for the shares of A and B and then calculate the shares of C by definition. – John Jul 7 '12 at 21:45