Add probability and quantile functions

[wleoncio]

After we've implemented the r* and d* functions, work on p* and q*. Both would probably be numerically determined (though analytical solutions are of course preferred).

Maybe one function can do the job for all distributions, since the procedure is similar see sketch below)?

prtrunclnorm <- function(q, meanlog = 0, sdlog = 1, lower.tail = TRUE, log.p = FALSE) {
  y <- rtrunc.lognormal(n = 1e3, ...)
  # bootstrap y
  # get value of y_0 of y corresponding to q
  # return probability from -Inf to y_0
}

and q* is basically the other way around.

• Implement ptrunc*
• Implement qtrunc*

[wleoncio]

A simpler solution, supposing prtrunclnorm(q, a) is the same as plnorm(q) - plnorm(a) is to do

prtrunclnorm <- function(..., a, b) {
  if (lower.tail) {
    return(plnorm(q) - plnorm(a))
  } else {
    return(plnorm(b) - plnorm(q))
  }
}

And the same goes for the other distros.

[rho62]

Yes, definitely a good suggestion. The only limitation I see, is if we have distributions, where the corresponing untruncated dist is not part of Base R (continuous Bernouilli, inverse Gamma)

…

18. jun. 2021 kl. 10:03 skrev Waldir Leoncio ***@***.***>: A simpler solution, supposing prtrunclnorm(q, a) is the same as plnorm(q) - plnorm(a) is to do prtrunclnorm <- function(..., a, b ) { if (lower.tail ) { return(plnorm(q) - plnorm(a )) } else { return(plnorm(b) - plnorm(q )) } } And the same goes for the other distros. — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub, or unsubscribe.

[wleoncio]

Removed this from 1.0.0 because it can be part of the MVP and, thus, a publication of a 0.1.0 version of the package.

Adding the prob and quantile functions might take a while, so I think it's a good idea to publish 0.1.0 as a milestone before adding these to an eventual 1.0.0.

[wleoncio]

Removed from MVP as agreed in our 2021-11-04 meeting. These functions are important, but not essential for the 1.0.0 launch.

[wleoncio]

Quantile functions

These will be calculated numerically. Use the CDF of a distribution (which increases monotonically) and find out which quantile gives the correct P(Y < y).

Probability functions

These should also be relatively straightforward, they are just a proportion C of their untruncated versions. See image below, with C in pink and the probability function in green.

Keep in mind that the integral limits, Lo and Hi, should in practice be the min/max between the truncation limit and the distribution support.

C is also used in all the density functions in this package, so it should probably be an auxiliary function to reduce code footprint.

[wleoncio]

Some relevant suggestions/comments can be found here and here.

[wleoncio]

Easy implementation from #80 (comment) (adapted, where X is a distribution name):

ptruncX(x; \theta) = (pX(x) - pX(a)) / pX(b) - pX(a)
qtruncX(x; \theta) = qX(p * (p * pX(b) + (1 - p) * pX(a)))

⚠️ Edit:

ptruncX(x; \theta) = (pX(x) - pX(a)) / (pX(b) - pX(a))
qtruncX(x; \theta) = qX(p * pX(b) + (1 - p) * pX(a))

[wleoncio]

Progress for ptrunc():

• Beta
• Binomial
• Chisq
• Contbernoulli
• Exp
• Gamma
• InvGamma
• InvGauss
• Log-Normal
• Negative Binomial
• Normal
• Poisson

[wleoncio]

Hi René,

Thanks again for providing me with the formulas. The one I was using previously (here, with corrections posted after "Edit") was wrong, which explains the issues I was having. The latest one you posted (here) have been implemented and seem to be working fine for Normal. I'll continue work on the remaining distros.