In Gaussian sum mixture model, any probability density function (pdf) can be written as a sum of Gaussian. Lets consider here any $n$-dimensional vector $x$ follows Gaussian distribution with mean $\hat{x} \in \mathbb{R}^n$, and covariance $P \in \mathbb{R}^{n\times n}$ can be written as \begin{equation} p(x) = \mathcal{N}(x;\, \hat{x},\, P) = \sum_{i=1}^{N_f} w_{i} \mathcal{N}(x;\, \hat{x}_i, \, P_i), \end{equation} where $w_i$ represents the weight of the $i$-th Gaussian pdf, and $\sum_{i=1}^{N_f} w_{i}=1$. $\hat{x}_i$ and $P_i$ are the $i$-th mean and covariance respectively. Here my specific question is how to generate $w_i$, $\hat{x}_i$ and $P_i$ for any $N_f$.
Any kind of suggestion will be of great help.