Simulated distributions [BE/BA News]

posted by Helmut Homepage – Vienna, Austria, 2022-05-02 13:43 (25 d 03:05 ago) – Posting: # 22950
Views: 337

Hi ElMaestro,

» 2. Do we use logs or not?

To get an idea about the simulated distributions, a large sample size and sampling every ten minutes. Shift of T –15 minutes, spread ±30 minutes.

[image]


Why do we see for T a high density in the first interval? Try this one:

roundClosest <- function(x, y) {
  res           <- y * round(x / y)
  res[res <= 0] <- y # Force negatives | 0 to the 1st interval
  return(res)
}
HL <- function(x, na.action = na.omit) {
  x   <- na.action(x)
  y   <- outer(x, x, "+")
  res <- median(y[row(y) >= col(y)]) / 2
  return(res)
}
n       <- 500
mu.tmax <- 1.5 # hours
CV.tmax <- 0.5
shift   <- -15 # minutes
spread  <- 30  # --"--
smpl    <- 10  # --"--
# Sample tmax of R from lognormal distribution
# parameterized for the median

R       <- rlnorm(n = n, meanlog = log(mu.tmax),
                         sdlog = sqrt(log(CV.tmax^2 + 1)))
# Introduce shift in location of T
shifts  <- runif(n = n, min = shift / 60 - spread / 60, # can be negative!
                        max = shift / 60 + spread / 60)
T       <- R + shifts
# Discretization by the sampling interval 'smpl'
R       <- roundClosest(R, smpl / 60)
T       <- roundClosest(T, smpl / 60)
res     <- data.frame(min    = rep(NA_real_, 3),
                      median = NA_real_,
                      HL     = NA_real_,
                      max    = NA_real_)
row.names(res)    <- c("R", "T", "T-R")
res[1, c(1:2, 4)] <- quantile(R, probs = c(0, 0.5, 1))
res[1, 3]         <- HL(R)
res[2, c(1:2, 4)] <- quantile(T, probs = c(0, 0.5, 1))
res[2, 3]         <- HL(T)
res[3, 2:3]       <- res[1, 2:3] - res[2, 2:3]
print(round(res, 5))

        min  median      HL     max
R   0.33333 1.50000 1.58333 7.00000
T   0.16667 1.33333 1.33333 6.66667
T-R      NA 0.16667 0.25000      NA


Since some shifts might be negative, I forced them to the first sampling interval – adding to the ones which are already there. Does that make sense?

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