$$ f_{\ell+1}=f_\ell-h\left(\log\left(\frac{1}{1-f}\right) - \frac{\sum^T_t\sum^N_i s_i(t)[\{f_\ell\}]}{T}\right) $$

$$ 1-\prod_i^N(1-\phi_f(\alpha_i)) $$

$$ \sum_{t=1}^T ( \sum_i s_i(t) - \mu)^2/T = \sum_{t=1}^T\left(\left(\sum_i s_i(t)\right)^2\right) $$

$$ \frac{\partial}{\partial \alpha_i}\left\{\mathcal{L}[\{s(t)\}\vert \{\new{\etav(t)}\}]+\lambda\left(\sum_{i=1}^N\alpha_i-1\right)\right\} $$

$$ \alpha_1 = 1 - \sum_{i=2}^N\alpha_i $$