# continuous: Univariate Continuous Distributions: p.d.f and c.d.f. In smovie: Some Movies to Illustrate Concepts in Statistics

 continuous R Documentation

## Univariate Continuous Distributions: p.d.f and c.d.f.

### Description

A movie to illustrate how the probability density function (p.d.f.) and cumulative distribution function (c.d.f.) of a continuous random variable depend on the values of its parameters.

### Usage

``````continuous(
distn,
var_range = 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,
...
)
``````

### Arguments

 `distn` Either a character string or a function to choose the continuous random variable. Strings `"beta"`, `"cauchy"`, `"chisq"` `"chi-squared"`, `"exponential"`, `"f"`, `"gamma"`, `"gev"`, `"gp"`, `"lognormal"`, `"log-normal"`, `"normal"`, `"t"`, `"uniform"` and `"weibull"` are recognised, case being ignored. The relevant distributional functions `dxxx` and `pxxx` in the `stats-package` are used. The abbreviations `xxx` are also recognised. The `"gev"` and `"gp"` cases use the `gev` and `gp` distributional functions in the `revdbayes` package. If `distn = "gamma"` then the `(shape, rate)` parameterisation is used, unless a value for `scale` is provided via the argument `params` when the `(shape, scale)` 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. If `distn` is not supplied then `distn = "normal"` is used. `var_range` A numeric vector of length 2. Can be used to set a fixed range of values over which to plot the p.d.f. and c.d.f., in order better to see the effects of changing the parameter values. If `var_range` 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. `"beta"`: `shape1 = 2, shape2 = 2, ncp = 0`; `"cauchy"`: `location = 0, scale = 1`; `"chi-squared"`: `df = 4, ncp = 0`; `"exponential"`: `rate = 1`; `"f"`: `df1 = 4, df2 = 8, ncp =0`; `"gamma"`: `shape = 2, rate = 1`; `"gev"`: `loc = 0, scale = 1, shape = 0.1`; `"gp"`: `loc = 0, scale = 1, shape = 0.1`; `"lognormal"`: `meanlog = 0, sdlog = 1`; `"normal"`: `mean = 0, sd = 1`; `"t"`: `df = 4, ncp = 0`; `"uniform"`: `min = 0, max = 1`; `"weibull"`: `shape = 2, scale = 1`. 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 100`p_vec[1]`% and 100`p_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. `...` Additional arguments to be passed to `rp.doublebutton`, not including `panel`, `variable`, `title`, `step`, `action`, `initval`, `range`.

### Details

The movie starts with a plot of the p.d.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.d.f. to the c.d.f. and back.

### Value

Nothing is returned, only the animation is produced.

`movies`: a user-friendly menu panel.

`smovie`: general information about smovie.

### Examples

``````# Normal example
continuous()
# Fix the range of values over which to plot
continuous(var_range = c(-10, 10))

# The same example, but using a user-supplied function and setting manually
# the initial parameters, parameter step size and range
continuous(distn = dnorm, params = list(mean = 0, sd = 1),
param_step = list(mean = 1, sd = 1),
param_range = list(sd = c(0, NA)))

# Gamma distribution. Show the use of var_range
continuous(distn = "gamma", var_range = c(0, 15))
``````

smovie documentation built on May 29, 2024, 10:28 a.m.