Lowercase vectorized normal distribution functions

Vectorized R wrappers for the scalar normal-kernel topics in this file. These helpers are meant for interactive use and examples rather than direct use inside NIMBLE code.

Usage

dnormmix(x, w, mean, sd, log = FALSE)

pnormmix(q, w, mean, sd, lower.tail = TRUE, log.p = FALSE)

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

rnormmix(n, w, mean, sd)

dnormmixgpd(x, w, mean, sd, threshold, tail_scale, tail_shape, log = FALSE)

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

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

rnormmixgpd(n, w, mean, sd, threshold, tail_scale, tail_shape)

dnormgpd(x, mean, sd, threshold, tail_scale, tail_shape, log = FALSE)

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

qnormgpd(
  p,
  mean,
  sd,
  threshold,
  tail_scale,
  tail_shape,
  lower.tail = TRUE,
  log.p = FALSE
)

rnormgpd(n, mean, sd, threshold, tail_scale, tail_shape)

Arguments

x

Numeric vector of quantiles.

w

Numeric vector of mixture weights.

mean, sd

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 vectorize the scalar normal-kernel routines for ordinary R use. They preserve the same formulas, parameter meanings, and tail construction as the uppercase functions; the only change is that x, q, p, and n may now be length greater than one.

For the mixture quantile and splice quantile functions, the numerical and piecewise logic is delegated directly to the corresponding scalar routine. As a result, the lowercase helpers are faithful front ends rather than separate implementations.

Functions

• dnormmix(): Normal mixture density (vectorized)

• pnormmix(): Normal mixture distribution function (vectorized)

• qnormmix(): Normal mixture quantile function (vectorized)

• rnormmix(): Normal mixture random generation (vectorized)

• dnormmixgpd(): Normal mixture + GPD density (vectorized)

• pnormmixgpd(): Normal mixture + GPD distribution function (vectorized)

• qnormmixgpd(): Normal mixture + GPD quantile function (vectorized)

• rnormmixgpd(): Normal mixture + GPD random generation (vectorized)

• dnormgpd(): Normal + GPD density (vectorized)

• pnormgpd(): Normal + GPD distribution function (vectorized)

• qnormgpd(): Normal + GPD quantile function (vectorized)

• rnormgpd(): Normal + GPD random generation (vectorized)

See also

normal_mix(), normal_mixgpd(), normal_gpd(), bundle(), get_kernel_registry().

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

Examples

w <- c(0.6, 0.25, 0.15)
mu <- c(-1, 0.5, 2)
sig <- c(1, 0.7, 1.3)

# Normal mixture
dnormmix(c(0, 1, 2), w = w, mean = mu, sd = sig)
#> [1] 0.26967693 0.17703568 0.06303415
rnormmix(5, w = w, mean = mu, sd = sig)
#> [1]  3.9212585 -1.3780286  1.5338650 -0.1731000  0.2224225

# Normal mixture + GPD
dnormmixgpd(c(1, 2, 3), w = w, mean = mu, sd = sig,
            threshold = 2, tail_scale = 1, tail_shape = 0.2)
#> [1] 0.17703568 0.07982551 0.02673340

# Normal + GPD (single component)
dnormgpd(c(1, 2, 3), mean = 0.5, sd = 1, threshold = 2,
         tail_scale = 1, tail_shape = 0.2)
#> [1] 0.3520653 0.0668072 0.0223736