How to get analytical formula of probability density function and cumulative distribution function for a distribution in R? - r

Is there anyway to print out the PDF/CDF formula for a distribution? E.g. for normal distribution I wish to run a command and see some formula printed f(x) = 1/sqrt(.....)...
I want to translate R's implementation of distributions like hyperbolic and EGB2 into Python and hope there is a way to fetch the formula from R elegantly rather than looking into the source code.

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Weighted mixture model of two distributions where weight depends on the value of the distribution?

I'm trying to replicate the precipitation mixture model from this paper: http://dx.doi.org/10.1029/2006WR005308
f(r) is the gamma PDF, g(r) is the generalized Pareto PDF, and w(r) is the weighting function, which depends on the value r being considered. I've looked at R packages like distr and mixtools that handle mixture models, but I only see examples where w is a constant, and I haven't found any implementations where the mixture is a function of the value. I'm struggling to create valid custom functions to represent h(r) so if someone could point me to a package that would be super helpful.

Find parameters such as the mean for any distribution in R

Is there any documentation, inside R, on the parameters and CDF/PDF of the most common distributions? I tried ?rexp but it doesn't provide the formula for the variance of X, only its mean.

R: functions to determine distance of multivariate data to normal distribution

I have a multivariate data and I am interested to compute the distance of complete data to multivariate normal distribution. I want to use R. I have seen some functions like shapiro-wilk test etc. But from them I can only understand if p-value is less <0.05 it does not follow normal distribution. But I want to know how much it is far from the normal distribution. Can anyone please refer me to some functions that I can refer to for use.
Use the mqqnorm function from the RVAideMemoire package. It shows, among others, Mahalanobis distances. From the function example:
x <- 1:30+rnorm(30)
y <- 1:30+rnorm(30,1,3)
mqqnorm(cbind(x,y))

Extract random sample from a unknown distribution (no generate stochastic random deviates)

I have a vector of data. I need build the density / distribution function and from that, extract a random sample, i.e. I need obtain the result that give us a function similar to rnorm(), rpois(), rbinom(), etc, but with a distribution built from a vector of data. All in R. Thank you so much.
It has nothing to do with generate stochastic random deviates.
I know the function sample() do something similar, but not exactly. If I use sample() I obtain only elements from my original data, as a discrete distribution and I need as a continuous distribution.

Numerical integration of numerical function in R

I'm, trying to apply this solution to find the p-value in an arbitrary distribution defined from data experiments. I have estimated this distribution using the density function in R. Now, I would like to integrate this function to apply the solution proposed by #mpiktas. However, the integrate function requires a function as input, not two vectors x and y with the values that define the function, which is what density provides.
Any idea on how to deal with this numerical integration based on x-y values in R?

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