Calculate "a" in c=sum_i( ( p(i)^a ) * b(i) ) / sum_i( p(i)^a )

[dalves]

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]

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"?

It's really hard to understand what you really meant without LaTeX, but if you meant

$\displaystyle{c=\frac{\sum p_i^a b_i}{\sum p_i^a}\Longrightarrow \sum p_i^a(c-b_i)=0}$ ...and this is as far as I can go without any further data.

DonAntonio

 

[dalves]

It's really hard to understand what you really meant without LaTeX, but if you meant

$\displaystyle{c=\frac{\sum p_i^a b_i}{\sum p_i^a}\Longrightarrow \sum p_i^a(c-b_i)=0}$ ...and this is as far as I can go without any further data.

DonAntonio

That is correct, I totally agree. The only further data is that "b(i)", "0 <= p(i) < 1" and "c" are known. I was hoping to be able to calculate "a" ... analytically.