How to implement a mixture model for Dirac Delta and Normal distributions? How could I fit data with observations from one Dirac delta component and $n$  normal distributed components?
Where $n$ usually is between 1 and 5.
My prior knowledge is that one component really is a Dirac delta distribution. I know its location in an $\mathbb{R}^2$ space.
I don't know the precise mean and not at all the variance of the normal distributed components.
Now I would like to find  mean and variance  of the normal distributed components and classify my data to be able to weight the components against each other.
Can you recommend any R packages for this?
I also considered julia's touring package or stan. As you see I am a novice in the realm and would be happy to devour any advice.

Assume that $X_i \sim \pi \delta_{x_0} + (1-\pi) N(\mu, \Sigma)$. If you know $x_0$, then, the natural estimate of $\pi$ is
$$
\hat \pi = \frac1n \sum_{i=1}^n 1\{X_i = x_0\}.
$$
You then fit a normal distribution to the rest of the data $\{X_i:\;X_i \neq x_0\}$ to get an estimate of $\mu$ and $\Sigma$.
