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\begin{document}

\SweaveOpts{engine=R,eps=FALSE}
%\VignetteIndexEntry{Plotting with plotpdf()}
%\VignetteDepends{gbutils}
%\VignetteKeywords{plot, pdf, cdf, quantiles}
%\VignettePackage{gbutils}

\setkeys{Gin}{width=0.4\textwidth}

<<echo=FALSE>>=
library(gbutils)
@

\title{Plotting with plotpdf()}
\author{Georgi N. Boshnakov}
\date{}
\maketitle

The function |plotpdf()| plots a function, usually probability density (pdf) or cumulative
distribution function (cdf), over an interval containing the ``interesting'' part of the
function. The interval is based on quantiles computed from a supplied cdf or quantile
function.

|plotpdf()| is most useful when the quantiles are not readily availaible but here are some
examples with a normal distribution to illustrate the idea:
<<>>=
pdf1 <- function(x) dnorm(x, mean = 100, sd = 5) # pdf
qdf1 <- function(x) qnorm(x, mean = 100, sd = 5) # qf
cdf1 <- function(x) pnorm(x, mean = 100, sd = 5) # cdf
@

|plot(pdf1)| works but needs arguments 'from' and 'to' for a meaningful plot.
We can simply pass the quantile function to |plotpdf()| to achieve this:
<<fig=TRUE>>=
plotpdf(pdf1, qdf1)
@

Similar result is obtained by supplying the cdf, which is handy when the quantiles are not
easily available:
<<fig=TRUE>>=
plotpdf(pdf1, cdf = cdf1)
@

By default, the lower and upper $0.01$ quantiles are used to set the limits on the $x$-axis.
This can be changed with arguments |lq| and |uq|
<<fig=TRUE>>=
plotpdf(pdf1, cdf = cdf1, lq = 0.001, uq = 0.999)
@

<<fig=TRUE>>=
plotpdf(cdf1, cdf = cdf1, lq = 0.001, uq = 0.999) # plot a cdf
@

The pdf and cdf of a mixture distribution are usually straight-forward. Here is an example:
<<>>=
pf1 <- function(x){
    0.25 * pnorm(x, mean = 3, sd = 0.2) + 0.75 * pnorm(x, mean = -1, sd = 0.5)
}
df1 <- function(x){
    0.25 * dnorm(x, mean = 3, sd = 0.2) + 0.75 * dnorm(x, mean = -1, sd = 0.5)
}
@

Here is a plot of the pdf:
<<fig=TRUE>>=
plotpdf(df1, cdf = pf1) # plot the pdf
@

... and this produces the cdf:
<<fig=TRUE>>=
plotpdf(pf1, cdf = pf1) # plot the cdf
@


Additional arguments can be specified as for |plot()|:
<<fig=TRUE>>=
plotpdf(pf1, cdf = pf1)                           # plot the cdf
plotpdf(df1, cdf = pf1, add = TRUE, col = "blue") # overlay the pdf
@

\bigskip{}

|plotpdf()| uses |cdf2quantile()| to compute quantiles from a cdf.
|cdf2quantile()| can be used directly, as well:
<<>>=
c(q5pc = cdf2quantile(0.05, pf1), q95pc = cdf2quantile(0.95, pf1))
@

\end{document}