The data sequence is generated from simulations using one algorithm. It should have the order $O(n^{\max{(\alpha, 1-\alpha)}})$. I know it can be approximately modeled as $a(n) = b_1n^{\alpha}+ b_2n^{1-\alpha}$ ($b_1,b_2$ are unknown constants) when $n$ is suffciently large.
I only care about the order $\max{(\alpha, 1-\alpha)}$ to justify the performance of the algorithm.
I have tried using $\frac{1}{t_1-t_0}\sum_{t=t_0+1}^{t_1}\log_2 \frac{a(2t)}{a(t)}$. The problem is the figure I got does not get the minimum at $\alpha = 0.5$.
I think the reason is that one of $b_1$ and $b_2$ is large, while the other is relatively small.
How to eliminate the numerical errors?