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Lowercase vectorized gamma distribution functions

gamma_lowercase.Rd

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

Usage

dgammamix(x, w, shape, scale, log = FALSE)

pgammamix(q, w, shape, scale, lower.tail = TRUE, log.p = FALSE)

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

rgammamix(n, w, shape, scale)

dgammamixgpd(
  x,
  w,
  shape,
  scale,
  threshold,
  tail_scale,
  tail_shape,
  log = FALSE
)

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

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

rgammamixgpd(n, w, shape, scale, threshold, tail_scale, tail_shape)

dgammagpd(x, shape, scale, threshold, tail_scale, tail_shape, log = FALSE)

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

qgammagpd(
  p,
  shape,
  scale,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE
)

rgammagpd(n, shape, scale, threshold, tail_scale, tail_shape)

Arguments

x

Numeric vector of quantiles.

w

Numeric vector of mixture weights.

shape, 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 wrappers are vectorized interfaces to the scalar gamma and gamma-plus-GPD routines. They preserve the package's shape-scale parameterization and the same splice definition used in the fitted-model prediction code. Quantile wrappers delegate to the scalar inversion code rather than implementing separate approximations.

Functions

  • dgammamix(): Gamma mixture density (vectorized)

  • pgammamix(): Gamma mixture distribution function (vectorized)

  • qgammamix(): Gamma mixture quantile function (vectorized)

  • rgammamix(): Gamma mixture random generation (vectorized)

  • dgammamixgpd(): Gamma mixture + GPD density (vectorized)

  • pgammamixgpd(): Gamma mixture + GPD distribution function (vectorized)

  • qgammamixgpd(): Gamma mixture + GPD quantile function (vectorized)

  • rgammamixgpd(): Gamma mixture + GPD random generation (vectorized)

  • dgammagpd(): Gamma + GPD density (vectorized)

  • pgammagpd(): Gamma + GPD distribution function (vectorized)

  • qgammagpd(): Gamma + GPD quantile function (vectorized)

  • rgammagpd(): Gamma + GPD random generation (vectorized)

See also

gamma_mix(), gamma_mixgpd(), gamma_gpd(), bundle(), get_kernel_registry().

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

Examples

w <- c(0.55, 0.3, 0.15)
shp <- c(2, 4, 6)
scl <- c(1, 2.5, 5)

# Gamma mixture
dgammamix(c(1, 2, 3), w = w, shape = shp, scale = scl)
#> [1] 0.2031918 0.1534717 0.0925686
rgammamix(5, w = w, shape = shp, scale = scl)
#> [1]  5.2491201 13.9246626  0.4627266 10.7429873 34.5715566

# Gamma mixture + GPD
dgammamixgpd(c(2, 3, 4), w = w, shape = shp, scale = scl,
             threshold = 3, tail_scale = 0.9, tail_shape = 0.2)
#> [1] 0.1534717 0.6104389 0.1831223

# Gamma + GPD (single component)
dgammagpd(c(2, 3, 4), shape = 4, scale = 2.5, threshold = 3,
          tail_scale = 0.9, tail_shape = 0.2)
#> [1] 0.0153371 1.0735900 0.3220605