Create convenience quantile functions for various probability distributions

[pierucci]

Should include:

• Binomial and multinomial variables.
• Beta and gamme density.
• Bounded density (e.g. non negative).
• Empirical density.
• RR, OR, HR...

[pierucci]

@KZARCA if you have any other suggestion regarding probability distribution that will be needed?

[KZARCA]

We should add lognormal and logit normal distributions, even if the latter
one is rarely used.

@KZARCA https://github.com/KZARCA if you have any other suggestion
regarding probability distribution that will be needed?

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#19 (comment).

[pierucci]

Support for Dirichlet distribution will be non trivial. Suggested implementation:

• Specify resampling from a multinomial distribution with r_multinomial();
• Specify which parameters belong to the same multinomial distribution with a define_multinomial() statement.

Example for {a, b, c} ~ Dirichlet(20, 30, 50) and {d, e} ~ Dirichlet(5, 10):

define_resample(
  a = r_multinomial(n = 20),
  b = r_multinomial(n = 30),
  c = r_multinomial(n = 50),

  d = r_multinomial(n = 5),
  e = r_multinomial(n = 10),

  define_multinomial(a, b, c),
  define_multinomial(d, e)
)

This implementation should check:

• That no parameter belong to more than one distribution;
• That all parameters belong to one distribution;
• That no parameter is correlated to anything else, not sure how to handle that correctly, or if it's even a good idea to handle that in the first place...

Programming:

• Ugly ugly string manipulation + parse();
• We will probably regret it eventually...

The define_multinomial() function will rescale multinomial parameters to sum to 1 by appending something like this to the dot-list:

a = a / (a+b+c),
b = b / (a+b+c),
c = c / (a+b+c),

d = d / (d+e),
e = e / (d+e)

[pierucci]

Actually solving everything UI-wise with a formula interface:

define_resample(
  a + b + c ~ multinom(20, 30, 50),
  d + e ~ multinom(5, 10),

# also works for standard distributions

  f ~ norm(0, 1)
)

Only the interface changed, the rest is the same behind the hood (and it's a mess, see #30).