Hello!
I have two normally distributed random variables $M \sim N(\mu_1,\sigma_1^2)$ and $V \sim N(\mu_2,\sigma_2^2)$ having physical meaning as $M$ - mass and $V$ - volume.
I need to figure out the corresponding p.d.f of variable $D$ - density (physical) given by formula $D=\frac{M}{V}$ (basic physical density formula). Combining those two densities seems wrong to me as they are of different physical dimensions and are connected by a nonlinear formula. So I tried sampling from both $M$ and $V$ distributions and then simply computing resulting density samples via the formula given above density_samples = mass_samples / volume_samples element-wise.
I was expecting the result to also be Gaussian Normal distribution, although the following pictures show its either skewed normal or some other distribution. I would like to model the density distribution $D$ as closely as possible in order to use it for estimation of components (Generally, the Gaussians $M$ and $V$ may be Gaussian Mixture Models, ergo the $D$ would also be a mixture).
Question
What is the proper way in modeling such distribution that are transformed by a nonlinear operation as division? ($D=\frac{M}{V}$). Is there some rule on how Normal Distribution behaves after non-linear transformation? (e.g. it becomes skewed or something like that?)
Figures
Normal Distribution of mass $M$
Normal Distribution of volume $V$
Unknown Distribution of density $D$
Looks like Skewed Normal Distribution
