Generates random variates from the geometric distribution by inversion. Optionally graphs the population cumulative distribution function and associated random variates, the population probability mass function and the empirical probability mass function of the random variates, and the empirical cumulative distribution function versus the population cumulative distribution function.
igeom(u = runif(1), prob,
minPlotQuantile = 0,
maxPlotQuantile = 0.95,
plot = TRUE,
showCDF = TRUE,
showPMF = FALSE,
showECDF = FALSE,
show = NULL,
plotDelay = 0,
maxPlotTime = 30,
resetRowsMargins = TRUE)vector of uniform(0,1) random numbers
probability of success in each trial (0 \(<\) prob \(\le\) 1)
controls the minimum quantile to appear in the plots
controls the maximum quantile to appear in the plots
logical; if TRUE (default), one or more plots will appear (see parameters below); otherwise no plots appear
logical; if TRUE (default), cdf plot appears, otherwise cdf plot is suppressed
logical; if FALSE (default), pmf plot is suppressed, otherwise pmf plot appears
logical; if FALSE (default), ecdf plot is suppressed, otherwise ecdf plot appears
shortcut way of denoting plots to display; either a binary vector of length three or an integer in [0,7] (see "Details" below)
delay, in seconds, between generation of the random variates
maximum time, in seconds, to plot all of the random variates
logical; if TRUE (default), resets the plot device to default rows and margins on exit
A vector of geometric random variates.
Generates random variates from the geometric distribution, and optionally, illustrates
the use of the inverse-cdf technique,
the effect of random sampling variability in relation to the pmf and cdf.
When all of the graphics are requested,
the top graph illustrates the use of the inverse-cdf technique by graphing the population cdf and the transformation of the random numbers to random variates,
the middle graph illustrates the effect of random sampling variability by graphing the population pmf and the empirical pmf associated with the random variates, and
the bottom graph illustrates effect of random sampling variability by graphing the population cdf and the empirical cdf associated with the random variates.
All aspects of the random variate generation algorithm are output in red. All aspects of the population distribution are output in black.
The geometric distribution with parameter prob = \(p\) has density
$$p(x) = p (1-p)^x$$
for \(x = 0, 1, 2, \ldots\), where \(0 < p \le 1\).
The algorithm for generating random variates from the geometric distribution is synchronized (one random variate for each random number) and monotone in u. This means that the variates generated here might be useful in some variance reduction techniques used in Monte Carlo and discrete-event simulation.
Values from the u vector are plotted in the cdf plot along the vertical axis as red dots. A horizontal, dashed, red line extends from the red dot to the population cdf. At the intersection, a vertical, dashed red line extends downward to the horizontal axis, where a second red dot, denoting the associated geometric random variate is plotted.
This is not a particularly fast variate generation algorithm because it uses
the base R qgeom function to invert the values contained in u.
All of the elements of the u vector must be between 0 and 1.
Alternatively, u can be NULL in which case plot(s) of the
theoretical pmf and cdf are displayed according to plotting parameter values
(defaulting to display of both the pmf and cdf).
The show parameter can be used as a shortcut way to denote plots to
display. The argument to show can be either:
a binary vector of length three, where the entries from left to right
correspond to showCDF, showPMF, and showECDF,
respectively. For each entry, a 1 indicates the plot should be
displayed, and a 0 indicates the plot should be suppressed.
an integer in [0,7] interpreted similar to Unix's chmod command. That is, the integer's binary representation can be transformed into a length-three vector discussed above (e.g., 6 corresponds to c(1,1,0)). See examples.
Any valid value for show takes precedence over existing individual
values for showCDF, showPMF, and showECDF.
The minPlotQuantile and maxPlotQuantile arguments are present in
order to compress the plots horizontally. The random variates generated are
not impacted by these two arguments. Vertical, dotted, black lines are
plotted at the associated quantiles on the plots.
The plotDelay and maxPlotTime arguments can be used to slow down
the variate generation for classroom explanation.
In the plot associated with the pmf, the maximum plotting height is associated with 125% of the maximum height of pmf. Any histogram cell that extends above this limit will have three black dots appearing above it.
# NOT RUN {
igeom(0.7, 0.4)
set.seed(8675309)
igeom(runif(10), 0.4, showPMF = TRUE)
set.seed(8675309)
igeom(runif(10), 0.4, showPMF = TRUE, showCDF = FALSE)
igeom(runif(120), 0.4, showPMF = TRUE, minPlotQuantile = 0.02, maxPlotQuantile = 0.98)
# show the PMF and CDF without any variates
igeom(NULL, 0.4)
# show CDF with inversion and PMF using show
igeom(runif(10), 0.4, show = c(1,1,0))
igeom(runif(10), 0.4, show = 6)
# show CDF with inversion and ECDF using show
igeom(runif(10), 0.4, show = c(1,0,1))
igeom(runif(10), 0.4, show = 5)
# show CDF with inversion, PMF, and ECDF using show
igeom(runif(10), 0.4, show = c(1,1,1))
igeom(runif(10), 0.4, show = 7)
# }
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