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The Empirical distribution

Source: R/Empirical.R
dempirical.Rd

Density (point mass), distribution, quantile function, as well as a random generation for the Empirical distribution.

Usage

dempirical(x, y, log = FALSE, na.rm = TRUE, method = NULL, ...)

pempirical(q, y, lower.tail = TRUE, log.p = FALSE, na.rm = TRUE)

qempirical(
  p,
  y,
  lower.tail = TRUE,
  log.p = FALSE,
  na.rm = TRUE,
  type = 1L,
  ...
)

rempirical(n, y, na.rm = TRUE)

Arguments

x

Vector of finite quantiles.

y

Vector of observations of the empirical distribution with two or more non-missing finite values.

log, log.p

logical. Indicates whether probabilities p are given as log(p) (both default to FALSE).

na.rm

logical indicating whether missing values (NA) are stripped before computation, defaults to TRUE.

method

NULL or one of "hist" or "density". If NULL, y is considered a random variable from a discrete empirical distribution. Method "hist" and "density" approximate a 'continuous' distribution based on the empirical sample y.

...

Allows to forward arguments to hist, density() and apply/sapply when calling dempirical() or sample quantile function when calling qempirical(). Else currently unused.

q

vector of quantiles.

lower.tail

logical indicating whether probabilities are \(P[X \le x]\) (lower tail) or \(P[X > x]\) (upper tail).

p

numeric vector of probabilities ([0, 1]).

type

integer, forwarded to quantile. Defaults to type = 1L.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

Details

All functions follow the usual conventions of d/p/q/r functions in base R. In particular, all four functions for the Empirical distribution call the corresponding *empirical functions.

See also

Other Empirical distribution: Empirical(), cdf.Empirical(), pdf.Empirical(), quantile.Empirical(), random.Empirical(), support.Empirical()

Examples

## Drawing two random empirical sample Y from the LogNormal distribution
## rounded to closest 0.5 (discrete)
set.seed(6020)
Y <- rlnorm(500L, meanlog = 1.5, sdlog = log(1.5))
Y <- round(Y * 2) / 2

bk <- seq(-0.25, 18.25, by = 1L)
hist(Y, freq = FALSE, breaks = bk, main = "Sample histogram")


x <- seq(0, 15, by = 0.5) # Quantiles
density <- dempirical(x, Y)
plot(density ~ x, type = "h", main = "Empirical density")


probability <- pempirical(x, Y)
plot(probability ~ x, type = "s", main = "Empirical distribution")


probs <- seq(0.01, 0.99, by = 0.01)
quantiles <- qempirical(probs, Y)
plot(probs ~ quantiles, type = "S", col = 2,
     main = "Empirical quantile function")


## Drawing random numbers (sampling with replacement)
set.seed(6020)
r <- rempirical(500L, Y)

hist(Y, freq = FALSE, breaks = bk, main = "Sample histogram")

hist(r, freq = FALSE, breaks = bk, main = "Random sample histogram")