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Lowercase vectorized inverse Gaussian distribution functions

invgauss_lowercase.Rd

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

Usage

dinvgaussmix(x, w, mean, shape, log = FALSE)

pinvgaussmix(q, w, mean, shape, lower.tail = TRUE, log.p = FALSE)

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

rinvgaussmix(n, w, mean, shape)

dinvgaussmixgpd(
  x,
  w,
  mean,
  shape,
  threshold,
  tail_scale,
  tail_shape,
  log = FALSE
)

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

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

rinvgaussmixgpd(n, w, mean, shape, threshold, tail_scale, tail_shape)

dinvgaussgpd(x, mean, shape, threshold, tail_scale, tail_shape, log = FALSE)

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

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

rinvgaussgpd(n, mean, shape, threshold, tail_scale, tail_shape)

Arguments

x

Numeric vector of quantiles.

w

Numeric vector of mixture weights.

mean, shape

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 functions are vectorized R front ends to the scalar inverse-Gaussian and splice routines. They retain the \((\mu,\lambda)\) parameterization used everywhere else in the package and apply the scalar evaluator repeatedly over the supplied input vector or draw index.

Functions

  • dinvgaussmix(): Inverse Gaussian mixture density (vectorized)

  • pinvgaussmix(): Inverse Gaussian mixture distribution function (vectorized)

  • qinvgaussmix(): Inverse Gaussian mixture quantile function (vectorized)

  • rinvgaussmix(): Inverse Gaussian mixture random generation (vectorized)

  • dinvgaussmixgpd(): Inverse Gaussian mixture + GPD density (vectorized)

  • pinvgaussmixgpd(): Inverse Gaussian mixture + GPD distribution function (vectorized)

  • qinvgaussmixgpd(): Inverse Gaussian mixture + GPD quantile function (vectorized)

  • rinvgaussmixgpd(): Inverse Gaussian mixture + GPD random generation (vectorized)

  • dinvgaussgpd(): Inverse Gaussian + GPD density (vectorized)

  • pinvgaussgpd(): Inverse Gaussian + GPD distribution function (vectorized)

  • qinvgaussgpd(): Inverse Gaussian + GPD quantile function (vectorized)

  • rinvgaussgpd(): Inverse Gaussian + GPD random generation (vectorized)

See also

InvGauss_mix(), InvGauss_mixgpd(), InvGauss_gpd(), bundle(), get_kernel_registry().

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

Examples

w <- c(0.6, 0.3, 0.1)
mu <- c(1, 1.5, 2)
lam <- c(2, 3, 4)

# Inverse Gaussian mixture
dinvgaussmix(c(1, 2, 3), w = w, mean = mu, shape = lam)
#> [1] 0.56238059 0.16823110 0.05436761
rinvgaussmix(5, w = w, mean = mu, shape = lam)
#> [1] 0.5447445 0.6622196 0.9414348 0.8989349 0.8352141