Univariate Discrete Distributions: p.m.f and c.d.f.

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.

Usage

discrete(
  distn,
  var_support = NULL,
  params = list(),
  param_step = list(),
  param_range = list(),
  p_vec = NULL,
  smallest = 0.01,
  plot_par = list(),
  panel_plot = TRUE,
  hscale = NA,
  vscale = hscale,
  observed_value = NA,
  ...
)

Arguments

distn

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.

var_support

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).

params

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.

param_step

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.

param_range

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.

p_vec

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).

smallest

A positive numeric scalar. The smallest value to be used for any strictly positive parameters when distn is a string.

plot_par

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.

panel_plot

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.

hscale, vscale

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.

observed_value

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.

Value

Nothing is returned, only the animation is produced.

Details

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.

Examples

# 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)