Lowercase vectorized Amoroso distribution functions

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

Usage

damorosomix(x, w, loc, scale, shape1, shape2, log = FALSE)

pamorosomix(q, w, loc, scale, shape1, shape2, lower.tail = TRUE, log.p = FALSE)

qamorosomix(
  p,
  w,
  loc,
  scale,
  shape1,
  shape2,
  lower.tail = TRUE,
  log.p = FALSE,
  tol = 1e-10,
  maxiter = 200
)

ramorosomix(n, w, loc, scale, shape1, shape2)

damorosomixgpd(
  x,
  w,
  loc,
  scale,
  shape1,
  shape2,
  threshold,
  tail_scale,
  tail_shape,
  log = FALSE
)

pamorosomixgpd(
  q,
  w,
  loc,
  scale,
  shape1,
  shape2,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE
)

qamorosomixgpd(
  p,
  w,
  loc,
  scale,
  shape1,
  shape2,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE,
  tol = 1e-10,
  maxiter = 200
)

ramorosomixgpd(
  n,
  w,
  loc,
  scale,
  shape1,
  shape2,
  threshold,
  tail_scale,
  tail_shape
)

damorosogpd(
  x,
  loc,
  scale,
  shape1,
  shape2,
  threshold,
  tail_scale,
  tail_shape,
  log = FALSE
)

pamorosogpd(
  q,
  loc,
  scale,
  shape1,
  shape2,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE
)

qamorosogpd(
  p,
  loc,
  scale,
  shape1,
  shape2,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE,
  tol = 1e-10,
  maxiter = 200
)

ramorosogpd(n, loc, scale, shape1, shape2, threshold, tail_scale, tail_shape)

Arguments

x

Numeric vector of quantiles.

w

Numeric vector of mixture weights.

loc, scale, shape1, shape2

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 are vectorized wrappers around the scalar Amoroso routines used internally by the package. They preserve the same location-scale-shape parameterization and the same piecewise splice logic for GPD tails. Quantile wrappers therefore continue to rely on the scalar numerical inversion or scalar GPD inverse exactly as documented for the uppercase functions.

Functions

• damorosomix(): Amoroso mixture density (vectorized)

• pamorosomix(): Amoroso mixture distribution function (vectorized)

• qamorosomix(): Amoroso mixture quantile function (vectorized)

• ramorosomix(): Amoroso mixture random generation (vectorized)

• damorosomixgpd(): Amoroso mixture + GPD density (vectorized)

• pamorosomixgpd(): Amoroso mixture + GPD distribution function (vectorized)

• qamorosomixgpd(): Amoroso mixture + GPD quantile function (vectorized)

• ramorosomixgpd(): Amoroso mixture + GPD random generation (vectorized)

• damorosogpd(): Amoroso + GPD density (vectorized)

• pamorosogpd(): Amoroso + GPD distribution function (vectorized)

• qamorosogpd(): Amoroso + GPD quantile function (vectorized)

• ramorosogpd(): Amoroso + GPD random generation (vectorized)

See also

amoroso_mix(), amoroso_mixgpd(), amoroso_gpd(), bundle(), get_kernel_registry().

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

Examples

w <- c(0.6, 0.3, 0.1)
locs <- c(0.5, 0.5, 0.5)
scls <- c(1, 1.3, 1.6)
s1 <- c(2.5, 3, 4)
s2 <- c(1.2, 1.2, 1.2)

# Amoroso mixture
damorosomix(c(1, 2, 3), w = w, loc = locs, scale = scls, shape1 = s1, shape2 = s2)
#> [1] 0.0961392 0.3047048 0.2651003
ramorosomix(5, w = w, loc = locs, scale = scls, shape1 = s1, shape2 = s2)
#> [1] 6.492420 1.686693 3.446359 4.104590 3.279362