R/Plot_Poisson_Density.R

In likanzhan/acqr: Functions Helping You understand Statistics Easily

#' Plot the density of a Poisson distribution
#' @export

Plot_Poisson_Density <- function(
                                 xx = 0:20,
                                 # lambda = 4
                                 lambda = c(4, 7, 10)) {
  plot_pdf <- function(lambda) {
    yy <- dpois(xx, lambda)
    xmax <- max(xx)
    ymax <- max(yy)
    plot(xx, yy,
      xlim = c(0, xmax + 0.3),
      type = "h", axes = FALSE, xlab = "", ylab = ""
    )
    box(col = "gray")
    axis(2, lwd = 0, lwd.ticks = 1, las = 1)
    points(xx, yy, pch = 16, col = "#6EA7CB", cex = 1.5)
    rect(xmax + 0.3, -1, xmax + 0.7, ymax + 1, col = "gray", border = "gray")
    text(xmax + 0.5, ymax / 2, srt = -90, label = bquote(labmda == .(lambda)))
  }
  plot_cdf <- function(lambda) {
    xs <- rep(xx, round(dpois(xx, lambda) * 100000, 0))
    yy <- ecdf(xs)
    xmax <- max(xx)
    ymax <- max(yy(xx))
    plot(yy, xlim = c(0, xmax + 0.3), ylab = "", axes = FALSE, col.points = "#6EA7CB", cex.points = 1.5, main = "")
    box(col = "gray")
    axis(2, lwd = 0, lwd.ticks = 1, las = 1)
    rect(xmax + 0.3, -1, xmax + 0.7, ymax + 1, col = "gray", border = "gray")
    text(xmax + 0.5, ymax / 2, srt = -90, label = bquote(lambda == .(lambda)))
  }
  par(
    mfcol = c(length(lambda), 2),
    mai = c(0.1, 0.6, 0, 0),
    oma = c(3, 0, 4, 0.2),
    pty = "m"
  )
  for (i in lambda) plot_pdf(lambda = i)
  axis(1, lwd = 0, lwd.ticks = 1)
  mtext(text = bquote(italic("x")), side = 1, line = 1.5, las = 1, outer = TRUE)
  mtext(
    text = bquote(bold(atop("PDF (probability density function)", italic(P(X == x[i]))))),
    side = 3, at = 0.25, las = 1, outer = TRUE
  )

  for (i in lambda) plot_cdf(lambda = i)
  axis(1, lwd = 0, lwd.ticks = 1)
  # mtext(text = expression("P(X"<="x)"), side = 4, outer = TRUE, at = 0.5, line = -18)
  mtext(
    text = bquote(bold(atop("CDF (cumulative distribution function)", italic(P(X <= x[i]))))),
    side = 3, at = 0.75, las = 1, outer = TRUE
  )
}
# Plot_Poisson_Density()