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Lowercase vectorized Laplace distribution functions

laplace_lowercase.Rd

Vectorized R wrappers for the scalar Laplace-kernel topics in this file.

Usage

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

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

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

rlaplacemix(n, w, location, scale)

dlaplacemixgpd(
  x,
  w,
  location,
  scale,
  threshold,
  tail_scale,
  tail_shape,
  log = FALSE
)

plaplacemixgpd(
  q,
  w,
  location,
  scale,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE
)

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

rlaplacemixgpd(n, w, location, scale, threshold, tail_scale, tail_shape)

dlaplacegpd(x, location, scale, threshold, tail_scale, tail_shape, log = FALSE)

plaplacegpd(
  q,
  location,
  scale,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE
)

qlaplacegpd(
  p,
  location,
  scale,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE
)

rlaplacegpd(n, location, scale, threshold, tail_scale, tail_shape)

Arguments

x

Numeric vector of quantiles.

w

Numeric vector of mixture weights.

location, scale

Numeric vectors (mix) or scalars (base+gpd) 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.

threshold, tail_scale, tail_shape

GPD tail parameters (scalars).

Value

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

Details

These helpers vectorize the scalar Laplace and Laplace-plus-GPD routines for interactive R use. They retain the same location-scale parameterization and the same splice definition as the uppercase functions. Quantiles continue to use the scalar root-finding or piecewise logic rather than a separate approximation.

Functions

  • dlaplacemix(): Laplace mixture density (vectorized)

  • plaplacemix(): Laplace mixture distribution function (vectorized)

  • qlaplacemix(): Laplace mixture quantile function (vectorized)

  • rlaplacemix(): Laplace mixture random generation (vectorized)

  • dlaplacemixgpd(): Laplace mixture + GPD density (vectorized)

  • plaplacemixgpd(): Laplace mixture + GPD distribution function (vectorized)

  • qlaplacemixgpd(): Laplace mixture + GPD quantile function (vectorized)

  • rlaplacemixgpd(): Laplace mixture + GPD random generation (vectorized)

  • dlaplacegpd(): Laplace + GPD density (vectorized)

  • plaplacegpd(): Laplace + GPD distribution function (vectorized)

  • qlaplacegpd(): Laplace + GPD quantile function (vectorized)

  • rlaplacegpd(): Laplace + GPD random generation (vectorized)

See also

laplace_mix(), laplace_MixGpd(), laplace_gpd(), bundle(), get_kernel_registry().

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

Examples

w <- c(0.6, 0.3, 0.1)
loc <- c(0, 1, -2)
scl <- c(1, 0.9, 1.1)

# Laplace mixture
dlaplacemix(c(-1, 0, 1), w = w, location = loc, scale = scl)
#> [1] 0.1467384 0.3622437 0.2800031
rlaplacemix(5, w = w, location = loc, scale = scl)
#> [1]  0.1896384  1.6330145 -0.7533515 -0.3716193  1.5012177