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require(distr)
options("newDevice"=TRUE)
Pause <- function() { cat("Hit <enter> to continue..."); readline()}
#################################################
## Comparison 1 - Exact, FFT and RtoDPQ
#################################################
N1 <- Norm(0,3)
N2 <- Norm(0,4)
rnew1 <- function(n) r(N1)(n) + r(N2)(n)
# calls exact formula -> N(0,5)
X <- N1 + N2
# calls FFT
Y <- N1 + as(N2, "AbscontDistribution")
# appoximation via RtoDPQ
Z <- new("AbscontDistribution", r = rnew1)
# density-plot
x <- seq(-15,15,0.01)
plot(x, d(X)(x), type = "l", lwd = 3, xlab = "", ylab = "density",
main = "Comparison 1", col = "black")
lines(x, d(Y)(x), col = "yellow")
lines(x, d(Z)(x), col = "red")
legend("topleft", legend = c("Exact", "FFT-Approximation",
"RtoDQP-Approximation"),
fill = c("black", "yellow", "red"))
Pause()
#################################################
## Comparison 2 - "Exact" Formula and RtoDPQ
#################################################
B <- Binom(size = 6, prob = 0.5) * 10
N <- Norm()
rnew2 <- function(n) r(B)(n) + r(N)(n)
# calls "exact" fomula
Y <- B + N
# appoximation via RtoDPQ
Z <- new("AbscontDistribution", r = rnew2)
# density-plot
x <- seq(-5,65,0.01)
plot(x, d(Y)(x), type = "l", xlab = "", ylab = "density",
main = "Comparison 2", col = "black")
lines(x, d(Z)(x), col = "red")
legend("topleft", legend = c("Exact", "RtoDQP-Approximation"),
fill = c("black", "red"))
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