CODEWITHSUNDEEP
rfunctionpdfplotcdf
user22456536
user22456536

Reputation: 23

Plotting CDF and PDF in R with custom function

I was wondering if there was any way to plot this PDF and CDF in R. I found these on a different question a user asked, and was curious.

pdfcdf

I know that I have to create a function and then plot this, but I'm struggling with the different parameters and am unsure how to translate this to R. I have only ever plotted PDF/CDF using a normal distribution, or from datasets.

Upvotes: 2

Views: 658

Answers (3)

ThomasIsCoding
ThomasIsCoding

Reputation: 101383

We can try the code below

f <- function(x) 0.5 * (x >= 0) + 0.5 * (x >= 1) - (x >= 1.5)
F <- Vectorize(function(x) integrate(f, -Inf, x)$value)

plot(f, -2, 2, col = "red")
curve(F, -2, 2, add = TRUE, col = "blue")
legend(-1, 0.8,
  legend = c("pdf", "cdf"),
  col = c("red", "blue"),
  lty = 1:2, cex = 2,
  box.col = "white"
)

enter image description here

Upvotes: 0

jay.sf
jay.sf

Reputation: 72828

ifelse can be very slow, we can fill an output vector instead. numeric() creates a vector of zeroes of a specified length, we then simply change everything that should not yield zero.

pdf_vec <- function(x) {
  out <- numeric(length(x))
  out[x >= 0 & x < 1] <- .5
  out[x >= 1 & x < 1.5] <- 1
  out
}

cdf_vec <- function(x) {
  out <- numeric(length(x))
  tmp <- x >= 0 & x < 1
  out[tmp] <- .5*x[tmp]
  tmp <- x >= 1 & x < 1.5
  out[tmp] <- x[tmp] - .5
  tmp <- x >= 1.5
  out[tmp] <- 1
  out
}

set.seed(42)
x <- rnorm(1e6)


stopifnot(all.equal(cdf(x), cdf1(x)))
stopifnot(all.equal(pdf(x), pdf1(x)))

@Allan Camero already showed nicely how to plot it.

Microbenchmark

It's about three times faster than the ifelse solution.

microbenchmark::microbenchmark(
  cdf_ifelse=cdf(x), cdf_vec=cdf1(x), check='equal'
)
# Unit: milliseconds
#       expr       min        lq     mean    median        uq       max neval cld
# cdf_ifelse 110.66285 121.25428 133.0789 133.86041 142.53296 167.64401   100   b
#    cdf_vec  43.56277  45.08759  48.8924  46.83869  49.46047  74.95487   100  a 

microbenchmark::microbenchmark(
  pdf_ifelse=pdf(x), pdf_vec=pdf1(x), check='equal'
)
# Unit: milliseconds
#       expr      min       lq      mean   median       uq      max neval cld
# pdf_ifelse 71.39501 76.71747 101.17738 81.43037 87.82162 192.3919   100   b
#    pdf_vec 27.82642 30.02056  34.55301 30.38457 31.29751 133.2798   100  a

Upvotes: 2

Allan Cameron
Allan Cameron

Reputation: 173813

You can write the pdf and cdf as functions, using ifelse to specify the values within the ranges, then simply plot the functions over the desired range:

pdf <- function(x) {
  ifelse(x >= 0 & x < 1, 0.5, ifelse(x < 1.5 & x >= 1, 1, 0))
}

cdf <- function(x) {
  ifelse(x < 0, 0,
         ifelse(x >= 0 & x < 1, 0.5 * x,
                ifelse(x < 1.5 & x >= 1, x - 0.5, 1)))
}

plot(pdf, xlim = c(-1, 2), type = "s")



plot(cdf, xlim = c(-1, 2))

Created on 2022-10-27 with reprex v2.0.2

Upvotes: 3

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