cdfPlot: Plot Cumulative Distribution Function

Description

Produce a cumulative distribution function (cdf) plot for a user-specified distribution.

Usage

cdfPlot(distribution = "norm", param.list = list(mean = 0, sd = 1), 
    left.tail.cutoff = ifelse(is.finite(supp.min), 0, 0.001), 
    right.tail.cutoff = ifelse(is.finite(supp.max), 0, 0.001), plot.it = TRUE, 
    add = FALSE, n.points = 1000, cdf.col = "black", cdf.lwd = 3 * par("cex"), 
    cdf.lty = 1, curve.fill = FALSE, curve.fill.col = "cyan", 
    digits = .Options$digits, ..., type = ifelse(discrete, "s", "l"), 
    main = NULL, xlab = NULL, ylab = NULL, xlim = NULL, ylim = NULL)

Arguments

distribution

a character string denoting the distribution abbreviation. The default value is distribution="norm". See the help file for Distribution.df for a list of possible distribution

param.list

a list with values for the parameters of the distribution. The default value is param.list=list(mean=0, sd=1). See the help file for Distribution.df for the names and possible

left.tail.cutoff

a numeric scalar indicating what proportion of the left-tail of the probability distribution to omit from the plot. For densities with a finite support minimum (e.g., Lognormal) the default value is 0

right.tail.cutoff

a scalar indicating what proportion of the right-tail of the probability 
  distribution to omit from the plot.  For densities with a finite support maximum 
  (e.g., Binomial) the default value is 0; fo

plot.it

a logical scalar indicating whether to create a plot or add to the existing plot 
  (see add) on the current graphics device.  If plot.it=FALSE, no 
  plot is produced, but a list of $(x, y)$ values is returned (see the section

add

a logical scalar indicating whether to add the cumulative distribution function curve 
  to the existing plot (add=TRUE), or to create a new plot 
  (add=FALSE; the default).  This argument is ignored if plot.it=FALSE

n.points

a numeric scalar specifying at how many evenly-spaced points the cumulative 
  distribution function will be evaluated.  The default value is n.points=1000.

cdf.col

a numeric scalar or character string determining 
  the color of the cdf line in the plot.  
  The default value is pdf.col="black".  See the entry for col in the 
  help file for par

cdf.lwd

a numeric scalar determining the width of the cdf 
  line in the plot.  
  The default value is pdf.lwd=3*par("cex").  
  See the entry for lwd in the help file for par 
  for more

cdf.lty

a numeric scalar determining the line type of 
  the cdf line in the plot.  
  The default value is pdf.lty=1.  See the entry for 
  lty in the help file for par for more informatio

curve.fill

a logical value indicating whether to fill in 
  the area below the cumulative distribution function curve with the color specified by 
  curve.fill.col.  The default value is curve.fill=FALSE.

curve.fill.col

when curve.fill=TRUE, a numeric scalar or character string 
  indicating what color to use to fill in the 
  area below the cumulative distribution function curve.  The default value is 
  curve.fill.col="cyan".  See the entry

digits

a scalar indicating how many significant digits to print for the distribution 
  parameters.  The default value is digits=.Options$digits.

type, main, xlab, ylab, xlim, ylim, ...

additional graphical parameters (see lines and par).  
  In particular, the argument type specifies the kind of line type.  
  By default, the funct

`Value`

cdfPlot invisibly returns a list giving coordinates of the points 
  that have been or would have been plotted:
QuantilesThe quantiles used for the plot.
Cumulative.ProbabilitiesThe values of the cdf associated with the quantiles.

`Details`

The cumulative distribution function (cdf) of a random variable $X$, 
  usually denoted $F$, is defined as:
  $$F(x) = Pr(X \le x) \;\;\;\;\;\; (1)$$
  That is, $F(x)$ is the probability that $X$ is less than or equal to 
  $x$.  This is the probability that the random variable $X$ takes on a 
  value in the interval $(-\infty, x]$ and is simply the (Lebesgue) integral of 
  the pdf evaluated between $-\infty$ and $x$. That is,
  $$F(x) = Pr(X \le x) = \int_{-\infty}^x f(t) dt \;\;\;\;\;\; (2)$$
  where $f(t)$ denotes the probability density function of $X$ 
  evaluated at $t$.  For discrete distributions, Equation (2) translates to 
  summing up the probabilities of all values in this interval:
  $$F(x) = Pr(X \le x) = \sum_{t \in (-\infty,x]} f(t) = \sum_{t \in (-\infty,x]} Pr(X = t) \;\;\;\;\;\; (3)$$

  A cumulative distribution function (cdf) plot plots the values of the 
  cdf against quantiles of the specified distribution.  Theoretical cdf plots 
  are sometimes plotted along with empirical cdf plots 
  to visually assess whether data have a particular distribution.

`References`

Forbes, C., M. Evans, N. Hastings, and B. Peacock. (2011).  Statistical Distributions. 
  Fourth Edition. John Wiley and Sons, Hoboken, NJ.

  Johnson, N. L., S. Kotz, and A.W. Kemp. (1992).  Univariate 
  Discrete Distributions, Second Edition.  John Wiley and Sons, New York.

  Johnson, N. L., S. Kotz, and N. Balakrishnan. (1994). 
  Continuous Univariate Distributions, Volume 1. 
  Second Edition. John Wiley and Sons, New York.
 
  Johnson, N. L., S. Kotz, and N. Balakrishnan. (1995). 
  Continuous Univariate Distributions, Volume 2. 
  Second Edition. John Wiley and Sons, New York.

`See Also`

Distribution.df, ecdfPlot, cdfCompare, 
  pdfPlot.

`Examples`

Run this code# Plot the cdf of the standard normal distribution 
  #-------------------------------------------------
  dev.new()
  cdfPlot()

  #==========

  # Plot the cdf of the standard normal distribution
  # and a N(2, 2) distribution on the sample plot. 
  #-------------------------------------------------
  dev.new()
  cdfPlot(param.list = list(mean=2, sd=2), main = "") 

  cdfPlot(add = TRUE, cdf.col = "red") 

  legend("topleft", legend = c("N(2,2)", "N(0,1)"), 
    col = c("black", "red"), lwd = 3 * par("cex")) 

  title("CDF Plots for Two Normal Distributions")
 
  #==========

  # Clean up
  #---------
  graphics.off()
Run the code above in your browser using DataLab