Produce a probability density function (pdf) plot for a user-specified distribution.
pdfPlot(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, pdf.col = "black",
pdf.lwd = 3 * par("cex"), pdf.lty = 1, curve.fill = !add,
curve.fill.col = "cyan", x.ticks.at.all.x.max = 15,
hist.col = ifelse(add, "black", "cyan"), density = 5,
digits = .Options$digits, ..., type = "l", main = NULL, xlab = NULL,
ylab = NULL, xlim = NULL, ylim = NULL)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 abbreviations.
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 values of the parameters
associated with each distribution.
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; for all other densities the default
value is 0.001.
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; for all other densities the
default value is 0.001.
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
VALUE below). The default value is plot.it=TRUE.
a logical scalar indicating whether to add the probability density 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.
a numeric scalar specifying at how many evenly-spaced points the probability
density function will be evaluated. The default value is n.points=1000.
for continuous distributions, a numeric scalar or character string determining
the color of the pdf line in the plot.
The default value is pdf.col="black". See the entry for col in the
help file for par for more information.
for continuous distributions, a numeric scalar determining the width of the pdf
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 information.
for continuous distributions, a numeric scalar determining the line type of
the pdf line in the plot.
The default value is pdf.lty=1. See the entry for
lty in the help file for par for more information.
for continuous distributions, a logical value indicating whether to fill in
the area below the probability density curve with the color specified by
curve.fill.col.
The default value is TRUE unless add=TRUE.
for continuous distributions, when curve.fill=TRUE,
a numeric scalar or character string
indicating what color to use to fill in the
area below the probability density curve. The default value is
curve.fill.col="cyan". See the entry for col in the
help file for par for more information.
a numeric scalar indicating the maximum number of ticks marks on the \(x\)-axis.
The default value is x.ticks.at.all.x.max=15.
for discrete distributions, a numeric scalar or character string indicating
what color to use to fill in the histogram if add=FALSE, or the color
of the shading lines if add=TRUE. The default is "cyan" if
add=FALSE and "black" if add=TRUE.
See the entry for col in the
help file for par for more information.
for discrete distributions, a scalar indicting the density of line shading for
the histogram when add=TRUE. This argument is ignored if add=FALSE.
a scalar indicating how many significant digits to print for the distribution
parameters. The default value is digits=.Options$digits.
additional graphical parameters. See plot.default and
par).
pdfPlot invisibly returns a list giving coordinates of the points
that have been or would have been plotted:
The quantiles used for the plot.
The values of the pdf associated with the quantiles.
The probability density function (pdf) of a random variable \(X\), usually denoted \(f\), is defined as: $$f(x) = \frac{dF(x)}{dx} \;\;\;\;\;\; (1)$$ where \(F\) is the cumulative distribution function (cdf) of \(X\). That is, \(f(x)\) is the derivative of the cdf \(F\) with respect to \(x\) (where this derivative exists).
For discrete distributions, the probability density function is simply: $$f(x) = Pr(X = x) \;\;\;\;\;\; (2)$$ In this case, \(f\) is sometimes called the probability function or probability mass function.
The probability that the random variable \(X\) takes on a value in the interval \([a, b]\) is simply the (Lebesgue) integral of the pdf evaluated between \(a\) and \(b\). That is, $$Pr(a \le X \le b) = \int_a^b f(x) dx \;\;\;\;\;\; (3)$$ For discrete distributions, Equation (3) translates to summing up the probabilities of all values in this interval: $$Pr(a \le X \le b) = \sum_{x \in [a,b]} f(x) = \sum_{x \in [a,b]} Pr(X = x) \;\;\;\;\;\; (4)$$
A probability density function (pdf) plot plots the values of the pdf against quantiles of the specified distribution. Theoretical pdf plots are sometimes plotted along with empirical pdf plots (density plots), histograms or bar graphs to visually assess whether data have a particular distribution.
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.
# NOT RUN {
# Plot the pdf of the standard normal distribution
#-------------------------------------------------
dev.new()
pdfPlot()
#==========
# Plot the pdf of the standard normal distribution
# and a N(2, 2) distribution on the sample plot.
#-------------------------------------------------
dev.new()
pdfPlot(param.list = list(mean=2, sd=2),
curve.fill = FALSE, ylim = c(0, dnorm(0)), main = "")
pdfPlot(add = TRUE, pdf.col = "red")
legend("topright", legend = c("N(2,2)", "N(0,1)"),
col = c("black", "red"), lwd = 3 * par("cex"))
title("PDF Plots for Two Normal Distributions")
#==========
# Clean up
#---------
graphics.off()
# }
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