Illustrated probability calculations from distributions

Usage

pdist(
  dist = "norm",
  q,
  plot = TRUE,
  verbose = FALSE,
  invisible = FALSE,
  digits = 3L,
  xlim,
  ylim,
  resolution = 500L,
  return = c("values", "plot"),
  ...,
  refinements = list()
)

xpgamma(
  q,
  shape,
  rate = 1,
  scale = 1/rate,
  lower.tail = TRUE,
  log.p = FALSE,
  ...
)

xpt(q, df, ncp, lower.tail = TRUE, log.p = FALSE, ...)

xpchisq(q, df, ncp = 0, lower.tail = TRUE, log.p = FALSE, ...)

xpf(q, df1, df2, lower.tail = TRUE, log.p = FALSE, ...)

xpbinom(q, size, prob, lower.tail = TRUE, log.p = FALSE, ...)

xppois(q, lambda, lower.tail = TRUE, log.p = FALSE, ...)

xpgeom(q, prob, lower.tail = TRUE, log.p = FALSE, ...)

xpnbinom(q, size, prob, mu, lower.tail = TRUE, log.p = FALSE, ...)

xpbeta(q, shape1, shape2, ncp = 0, lower.tail = TRUE, log.p = FALSE, ...)

Arguments

dist: a character description of a distribution, for example "norm", "t", or "chisq"
q: a vector of quantiles
plot: a logical indicating whether a plot should be created
verbose: a logical
invisible: a logical
digits: the number of digits desired
xlim: x limits
ylim: y limits
resolution: Number of points used for detecting discreteness and generating plots. The default value of 5000 should work well except for discrete distributions that have many distinct values, especially if these values are not evenly spaced.
return: If "plot", return a plot. If "values", return a vector of numerical values.
...: Additional arguments, typically for fine tuning the plot.
refinements: A list of refinements to the plot. See ggformula::gf_refine().
shape, scale: shape and scale parameters. Must be positive, scale strictly.
rate: an alternative way to specify the scale.
lower.tail: logical; if TRUE (default), probabilities are \(P[X < x]\), otherwise, \(P[X \ge x]\) (exceptionally not cadlag here, to ensure, e.g., pgamma(0, shape=0) remains zero).
log.p: A logical indicating whether probabilities should be returned on the log scale.
df: degrees of freedom (\(> 0\), maybe non-integer). df = Inf is allowed.
ncp: non-centrality parameter \(\delta\); currently except for rt(), accurate only for abs(ncp) <= 37.62. If omitted, use the central \(t\) distribution.
df1, df2: degrees of freedom. Inf is allowed.
size: number of trials (zero or more).
prob: probability of success on each trial.
lambda: vector of (non-negative) means.
mu: alternative parametrization via mean: see ‘Details’.
shape1, shape2: non-negative parameters of the Beta distribution.

Value

A vector of probabilities; a plot is printed as a side effect.

Details

The most general function is pdist which can work with any distribution for which a p-function exists. As a convenience, wrappers are provided for several common distributions.

Examples

pdist("norm", -2:2)

#> [1] 0.02275013 0.15865525 0.50000000 0.84134475 0.97724987
pdist("norm", seq(80,120, by = 10), mean = 100, sd = 10)

#> [1] 0.02275013 0.15865525 0.50000000 0.84134475 0.97724987
pdist("chisq", 2:4, df = 3)

#> [1] 0.4275933 0.6083748 0.7385359
pdist("f", 1, df1 = 2, df2 = 10)

#> [1] 0.5981224
pdist("gamma", 2, shape = 3, rate = 4)

#> [1] 0.986246