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Lowercase vectorized Cauchy mixture distribution functions

cauchy_mix_lowercase.Rd

Vectorized R wrappers for the scalar Cauchy mixture functions in this file.

Usage

dcauchymix(x, w, location, scale, log = FALSE)

pcauchymix(q, w, location, scale, lower.tail = TRUE, log.p = FALSE)

qcauchymix(
  p,
  w,
  location,
  scale,
  lower.tail = TRUE,
  log.p = FALSE,
  tol = 1e-10,
  maxiter = 200
)

rcauchymix(n, w, location, scale)

Arguments

x

Numeric vector of quantiles.

w

Numeric vector of mixture weights.

location, scale

Numeric vectors of component parameters.

log

Logical; if TRUE, return log-density.

q

Numeric vector of quantiles.

lower.tail

Logical; if TRUE (default), probabilities are \(P(X \le x)\).

log.p

Logical; if TRUE, probabilities are on log scale.

p

Numeric vector of probabilities.

tol, maxiter

Tolerance and max iterations for numerical inversion.

n

Integer number of observations to generate.

Value

Numeric vector of densities, probabilities, quantiles, or random variates.

Details

These are vectorized R wrappers around the scalar Cauchy-mixture routines. They retain the same location-scale parameterization and the same inverse-CDF logic for simulation and quantiles. The lowercase functions do not alter the heavy-tail theory of the underlying Cauchy components; they apply the scalar routines elementwise to vector inputs in R.

Functions

  • dcauchymix(): Cauchy mixture density (vectorized)

  • pcauchymix(): Cauchy mixture distribution function (vectorized)

  • qcauchymix(): Cauchy mixture quantile function (vectorized)

  • rcauchymix(): Cauchy mixture random generation (vectorized)

See also

cauchy_mix(), cauchy(), bundle(), get_kernel_registry().

Other vectorized kernel helpers: amoroso_lowercase, base_lowercase, gamma_lowercase, invgauss_lowercase, laplace_lowercase, lognormal_lowercase, normal_lowercase

Examples

w <- c(0.6, 0.3, 0.1)
loc <- c(-1, 0, 1)
scl <- c(1, 1.2, 2)

dcauchymix(c(-2, 0, 2), w = w, location = loc, scale = scl)
#> [1] 0.12145467 0.18780283 0.05289561
rcauchymix(5, w = w, location = loc, scale = scl)
#> [1]  0.2741499 -1.6557906 -0.9004822  0.2034606 -0.2070826