Lowercase vectorized lognormal distribution functions

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

Usage

dlognormalmix(x, w, meanlog, sdlog, log = FALSE)

plognormalmix(q, w, meanlog, sdlog, lower.tail = TRUE, log.p = FALSE)

qlognormalmix(
  p,
  w,
  meanlog,
  sdlog,
  lower.tail = TRUE,
  log.p = FALSE,
  tol = 1e-10,
  maxiter = 200
)

rlognormalmix(n, w, meanlog, sdlog)

dlognormalmixgpd(
  x,
  w,
  meanlog,
  sdlog,
  threshold,
  tail_scale,
  tail_shape,
  log = FALSE
)

plognormalmixgpd(
  q,
  w,
  meanlog,
  sdlog,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE
)

qlognormalmixgpd(
  p,
  w,
  meanlog,
  sdlog,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE,
  tol = 1e-10,
  maxiter = 200
)

rlognormalmixgpd(n, w, meanlog, sdlog, threshold, tail_scale, tail_shape)

dlognormalgpd(
  x,
  meanlog,
  sdlog,
  threshold,
  tail_scale,
  tail_shape,
  log = FALSE
)

plognormalgpd(
  q,
  meanlog,
  sdlog,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE
)

qlognormalgpd(
  p,
  meanlog,
  sdlog,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE
)

rlognormalgpd(n, meanlog, sdlog, threshold, tail_scale, tail_shape)

Arguments

x

Numeric vector of quantiles.

w

Numeric vector of mixture weights.

meanlog, sdlog

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 direct vectorized wrappers around the scalar lognormal routines. They keep the same parameterization, support restrictions, and bulk-tail splice, while allowing ordinary vector inputs in R. Quantile wrappers continue to use the scalar inversion logic, so there is no separate approximation layer in the lowercase API.

Functions

• dlognormalmix(): Lognormal mixture density (vectorized)

• plognormalmix(): Lognormal mixture distribution function (vectorized)

• qlognormalmix(): Lognormal mixture quantile function (vectorized)

• rlognormalmix(): Lognormal mixture random generation (vectorized)

• dlognormalmixgpd(): Lognormal mixture + GPD density (vectorized)

• plognormalmixgpd(): Lognormal mixture + GPD distribution function (vectorized)

• qlognormalmixgpd(): Lognormal mixture + GPD quantile function (vectorized)

• rlognormalmixgpd(): Lognormal mixture + GPD random generation (vectorized)

• dlognormalgpd(): Lognormal + GPD density (vectorized)

• plognormalgpd(): Lognormal + GPD distribution function (vectorized)

• qlognormalgpd(): Lognormal + GPD quantile function (vectorized)

• rlognormalgpd(): Lognormal + GPD random generation (vectorized)

See also

lognormal_mix(), lognormal_mixgpd(), lognormal_gpd(), bundle(), get_kernel_registry().

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

Examples

w <- c(0.6, 0.3, 0.1)
ml <- c(0, 0.3, 0.6)
sl <- c(0.4, 0.5, 0.6)

# Lognormal mixture
dlognormalmix(c(1, 2, 3), w = w, meanlog = ml, sdlog = sl)
#> [1] 0.8386766 0.1873719 0.0425651
rlognormalmix(5, w = w, meanlog = ml, sdlog = sl)
#> [1] 0.6360860 0.7556021 1.5831195 1.4558284 0.5728457

# Lognormal mixture + GPD
dlognormalmixgpd(c(2, 3, 4), w = w, meanlog = ml, sdlog = sl,
                 threshold = 2.5, tail_scale = 0.5, tail_shape = 0.2)
#> [1] 0.187371921 0.046321740 0.008244275