Fundamental Graphics in R

Prof. Ke-Sheng Cheng

Dept. of Bioenvironmental Systems Eng.

National Taiwan University

Histogram

• hist(x, freq=FALSE, breaks=…)– breaks=• a vector giving the breakpoints between histogram cells, • a single number giving the number of cells for the

histogram.

– freq=• If TRUE, the histogram graphic is a representation of

frequencies, the counts component of the result,• if FALSE, probability densities, component density, are

plotted (so that the histogram has a total area of one).

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Empirical CDF, ecdf

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• The ecdf in R is a function.

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Sample quantiles

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Linear interpolation

Using the quantile function to calculate sample quantiles

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Not linear interpolation!

These three numbers define the box. Whiskers are defined differently.

The QQ plots

• The quantile-quantile plots are a type of scatter plot used to compare distributions of two groups or to compare a sample with a reference distribution.

• When the groups are of different sizes, R reduces the size of the larger group to the size of the smaller one by keeping the minimum and maximum values, and choosing equally spaced quantiles between.

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The boxplot in R• boxplot(x,range=0)• boxplot(x) [Default, range=1.5]• boxplot(x,range=3)• A box-and-whisker plot includes two major parts – the

box and the whiskers.• The parameter range determines how far the plot whiskers extend out from the box. If range is positive, the whiskers extend to the most extreme data point which is no more than range times the interquartile range from the box. A value of zero causes the whiskers to extend to the data extremes.

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•

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Comparison of multiple boxplots

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Can also useboxplot(x1,x2,x3,names=c(“x1”, ”x2”, ”x3”))

• Comparison of multiple boxplots

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Low-level graphics

• In R graphics, the display is divided into:– The plot region where data will be drawn– Four margin areas, numbered clockwise from 1 to 4,

starting at the bottom.

• After establishing the plot region and margins, we can start adding points, lines, polygons, and symbols to the plot region.

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• Graphic components– points(x,y, …)– lines(x,y, …)– text(x,y, labels, …)– abline(a,b, …) # adds the line y=a+bx– abline(h=y, …)– abline(v=x, …)– polygon(x,y, …)– segments(x0,y0,x1,y1, …)– arrows(x0,y0,x1,y1, …)– symbols(x,y, …)– legend(x,y, legend, …)

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Saving Graphs to Files

• The R graphics display can consists of various graphics devices. The default device is the screen. However, it is also possible to save a graph to a file by assigning other graphics devices.

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• Assigning R graphics device – a pdf file

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Use > jpg(“filename.jpg”), if you want to save a graph to a jpeg file.

Random number generation in R• R commands for stochastic simulation (for

normal distribution – pnorm – cumulative probability– qnorm – quantile function– rnorm – generating a random sample of a specific

sample size– dnorm – probability density function

For other distributions, simply change the distribution names. For examples, (punif, qunif, runif, and dunif) for uniform distribution and (ppois, qpois, rpois, and dpois) for Poisson distribution.

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Approximation of the Poisson distribution by normal distribution

Demonstration using stochastic simulation

• Using R

)20,20()20( 2 NPoisson

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20251]25[

XP

.

Estimated by normal approximation of Poisson distribution

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Poisson CDF by stochastic simulation

Estimated by stochastic simulation of Poisson distribution

Direct calculation using theoretical CDF of Poisson distribution.

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Approximation by normal distribution

Poisson CDF by stochastic simulation

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3-D Graphics

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