Illustrated quantile calculations from distributions

Usage

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

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

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

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

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

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

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

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

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

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

Arguments

dist: a character description of a distribution, for example "norm", "t", or "chisq"
p: a vector of probabilities
plot: a logical indicating whether a plot should be created
verbose: a logical
invisible: a logical
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.
digits: the number of digits desired
xlim: x limits. By default, these are chosen to show the central 99.8\ of the distribution.
ylim: y limits
return: If "plot", return a plot. If "values", return a vector of numerical values.
refinements: A list of refinements to the plot. See ggformula::gf_refine().
...: additional arguments, including parameters of the distribution and additional options for the plot. To help with name collisions (eg size for binomial distributions and shape for gamma distributions), argument names beginning plot_ will be renamed to remove plot_ and passed only to the plot. The unprefixed version will used as a parameter for the the distribution.
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 quantiles; a plot is printed as a side effect

Details

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

Examples

qdist("norm", seq(.1, .9, by = 0.10), 
      title = "Deciles of a normal distribution", show.legend = FALSE,
      pattern = "rings")

#> [1] -1.2815516 -0.8416212 -0.5244005 -0.2533471  0.0000000  0.2533471  0.5244005
#> [8]  0.8416212  1.2815516
xqnorm(seq(.2, .8, by = 0.20), mean = 100, sd = 10)
#> 
#> If X ~ N(100, 10), then 
#> 	P(X <=  91.58379) = 0.2	P(X <=  97.46653) = 0.4	P(X <= 102.53347) = 0.6	P(X <= 108.41621) = 0.8
#> 	P(X >   91.58379) = 0.8	P(X >   97.46653) = 0.6	P(X >  102.53347) = 0.4	P(X >  108.41621) = 0.2
#> 

#> [1]  91.58379  97.46653 102.53347 108.41621
qdist("unif", .5)

#> [1] 0.5
xqgamma(.5, shape = 3, scale = 4)

#> [1] 10.69624
xqgamma(.5, shape = 3, scale = 4, color = "black")

#> [1] 10.69624
xqbeta(.5, shape1 = .9, shape2 = 1.4, dlwd = 1)

#> [1] 0.3557401
xqchisq(c(.25,.5,.75), df = 3)

#> [1] 1.212533 2.365974 4.108345
xcbinom(c(0.80, 0.90), size = 1000, prob = 0.40)

#> [1] 375 380 420 426
# displayed as if continuous
xcbinom(c(0.80, 0.90), size = 5000, prob = 0.40)

#> [1] 1943 1956 2044 2057
xpbinom(c(480, 500, 520), size = 1000, prob = 0.48)

#> [1] 0.5127908 0.9027460 0.9948015
xpbinom(c(40, 60), size = 100, prob = 0.5)

#> [1] 0.02844397 0.98239990
xqpois(c(0.25, 0.5, 0.75), lambda = 12)

#> [1] 10 12 14
xcpois(0.50, lambda = 12)

#> [1] 10 14
xcpois(0.50, lambda = 12, refinements = list(scale_color_brewer(type = "qual", palette = 5)))
#> Scale for colour is already present.
#> Adding another scale for colour, which will replace the existing scale.

#> [1] 10 14