A movie to illustrate how the probability mass function (p.m.f.) and cumulative distribution function (c.d.f.) of a discrete random variable depend on the values of its parameters.
Either a character string or a function to choose the discrete random variable.
Strings "binomial", "geometric",
"hypergeometric", "negative binomial" and "poisson"
are recognised, case being ignored. The relevant distributional functions
dxxx and pxxx in the stats-package
are used. The abbreviations xxx are also recognised.
If distn = "negative binomial" then the (size, prob)
parameterisation is used, unless a value for mu is provided
via the argument params when the (size, mu)
parameterisation is used.
Valid functions are set up like a standard distributional function
dxxx, with first argument x, last argument log
and with arguments to set the parameters of the distribution in between.
See the
CRAN task view on distributions.
It is assumed that the support of the random variable is a
subset of the integers, unless var_support is set to the contrary.
If distn is not supplied then distn = "binomial"
is used.
A numeric vector. Can be used to set a fixed set of
values for which to plot the p.m.f. and c.d.f., in order better
to see the effects of changing the parameter values or to set a support
that isn't a subset of the integers.
If var_support is set then it overrides p_vec (see below).
A named list of initial parameter values with which to start
the movie. If distn is a string and a particular parameter value
is not supplied then the following values are used.
"binomial": size = 10, prob = 0.5;
"geometric": prob = 0.5;
"hypergeometric": m = 10, n = 7, k = 8;
"negative binomial": size = 10, prob = 0.5;
"poisson": lambda = 5.
If distn is a function then params must set any required
parameters.
If parameter value is outside the corresponding range specified by
param_range then it is set to the closest limit of the range.
A named list of the amounts by which the respective
parameters in params are increased/decreased after one click of
the +/- button. If distn is a function then the default is 0.1
for all parameters. If distn is a string then a sensible
distribution-specific default is set internally.
A named list of the ranges over which the respective
parameters in params are allowed to vary. Each element of the list
should be a vector of length 2: the first element gives the lower limit
of the range, the second element the upper limit.
Use NA to impose no limit.
If distn is a function then all parameters are unconstrained.
A numeric vector of length 2. The p.d.f. and c.d.f. are
plotted between the 100p_vec[1]% and 100p_vec[2]%
quantiles of the distribution. If p_vec is not supplied then
a sensible distribution-specific default is used. If distn is
a function then the default is p_vec = c(0.001, 0.999).
A positive numeric scalar. The smallest value to be
used for any strictly positive parameters when distn is a string.
A named list of graphical parameters
(see par) to be passed to
plot. This may be used to alter the
appearance of the plots of the p.m.f. and c.d.f.
A logical parameter that determines whether the plot
is placed inside the panel (TRUE) or in the standard graphics
window (FALSE). If the plot is to be placed inside the panel
then the tkrplot library is required.
Numeric scalars. Scaling parameters for the size
of the plot when panel_plot = TRUE. The default values are 1.4 on
Unix platforms and 2 on Windows platforms.
A non-negative integer. If observed_value is
supplied then the corresponding line in the plot of the p.m.f. is coloured
in red.
Additional arguments to be passed to
rp.doublebutton, not including panel,
variable, title, step, action, initval,
range.
Nothing is returned, only the animation is produced.
The movie starts with a plot of the p.m.f. of the distribution for the initial values of the parameters. Buttons increase (+) or decrease (-) each parameter. There are radio buttons to switch the plot from the p.m.f. to the c.d.f. and back.
If distn == "geometric" then there are radio buttons to switch
between the version of the the geometric distribution based on the
number of trials up to including the first success and the number of
failures until the first success.
Owing to a conflict with the argument size of the function
rp.control the parameter size of,
for example, the binomial and negative binomial distributions, is
labelled as n.
# Binomial example
discrete()
# The same example, but using a user-supplied function and setting manually
# the initial parameters, parameter step size and range
discrete(distn = dbinom, params = list(size = 10, prob = 0.5),
param_step = list(size = 1),
param_range = list(size = c(1, NA), prob = c(0, 1)))
# Poisson distribution. Show the use of var_support
discrete(distn = "poisson", var_support = 0:20)