Cauchy Distribution

Usage

Cauchy(location = 0, scale = 1)

# S4 method for class 'Cauchy,numeric'
d(distr, x)

# S4 method for class 'Cauchy,numeric'
p(distr, x)

# S4 method for class 'Cauchy,numeric'
qn(distr, x)

# S4 method for class 'Cauchy,numeric'
r(distr, n)

# S4 method for class 'Cauchy'
mean(x)

# S4 method for class 'Cauchy'
median(x)

# S4 method for class 'Cauchy'
mode(x)

# S4 method for class 'Cauchy'
var(x)

# S4 method for class 'Cauchy'
sd(x)

# S4 method for class 'Cauchy'
skew(x)

# S4 method for class 'Cauchy'
kurt(x)

# S4 method for class 'Cauchy'
entro(x)

# S4 method for class 'Cauchy'
finf(x)

llcauchy(x, location, scale)

# S4 method for class 'Cauchy,numeric'
ll(distr, x)

ecauchy(x, type = "mle", ...)

# S4 method for class 'Cauchy,numeric'
mle(
  distr,
  x,
  par0 = "me",
  method = "L-BFGS-B",
  lower = c(-Inf, 1e-05),
  upper = c(Inf, Inf)
)

# S4 method for class 'Cauchy,numeric'
me(distr, x)

vcauchy(location, scale, type = "mle")

# S4 method for class 'Cauchy'
avar_mle(distr)

Arguments

location, scale: numeric. The distribution parameters.
distr: an object of class Cauchy.
x: an object of class Cauchy. If the function also has a distr argument, x is a numeric vector, a sample of observations.
n: numeric. The sample size.
type: character, case ignored. The estimator type (mle, me, or same).
...: extra arguments.
par0, method, lower, upper: arguments passed to optim.

Value

Each type of function returns a different type of object:

Distribution Functions: When supplied with one argument (distr), the d(), p(), q(), r(), ll() functions return the density, cumulative probability, quantile, random sample generator, and log-likelihood functions, respectively. When supplied with both arguments (distr and x), they evaluate the aforementioned functions directly.
Moments: Returns a numeric, either vector or matrix depending on the moment and the distribution. The moments() function returns a list with all the available methods.
Estimation: Returns a list. The estimator of the unknown parameters. Note that in distribution families like the binomial, multinomial, and negative binomial, the size is not returned, since it is considered known.
Variance: Returns a named matrix. The asymptotic covariance matrix of the estimator.