The equation c = sum_i( ( p(i)^a ) * b(i) ) / sum_i( p(i)^a ) is used to calculate the variable "a" when "c", "b(i)", and "p(i)" are known. The transformation of the equation leads to the form sum p_i^a(c - b_i) = 0, which indicates that the solution for "a" requires further data or constraints. The discussion emphasizes the challenge of deriving "a" analytically without additional information on the variables involved.
PREREQUISITESMathematicians, data scientists, and analysts involved in statistical modeling and parameter estimation will benefit from this discussion.
dalves said:In the following equation:
c = sum_i( ( p(i)^a ) * b(i) ) / sum_i( p(i)^a )
"c", "0 <= p(i) < 1" and "b(i)" are known.
How do I calculate "a"?
DonAntonio said:It's really hard to understand what you really meant without LaTeX, but if you meant
[itex]\displaystyle{c=\frac{\sum p_i^a b_i}{\sum p_i^a}\Longrightarrow \sum p_i^a(c-b_i)=0}[/itex] ...and this is as far as I can go without any further data.
DonAntonio