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Weighted normal distribution

Source: R/distributions.R
weighted_normal.Rd

Density, distribution function, quantile function and random generation for the weighted normal distribution with mean, standard deviation sd, steps steps (or critical values) crit_x), and weights omega.

Usage

dwnorm(
  x,
  mean,
  sd,
  steps = if (!is.null(crit_x)) NULL,
  omega,
  crit_x = if (!is.null(steps)) NULL,
  type = "two.sided",
  log = FALSE
)

pwnorm(
  q,
  mean,
  sd,
  steps = if (!is.null(crit_x)) NULL,
  omega,
  crit_x = if (!is.null(steps)) NULL,
  type = "two.sided",
  lower.tail = TRUE,
  log.p = FALSE
)

qwnorm(
  p,
  mean,
  sd,
  steps = if (!is.null(crit_x)) NULL,
  omega,
  crit_x = if (!is.null(steps)) NULL,
  type = "two.sided",
  lower.tail = TRUE,
  log.p = FALSE
)

rwnorm(
  n,
  mean,
  sd,
  steps = if (!is.null(crit_x)) NULL,
  omega,
  crit_x = if (!is.null(steps)) NULL,
  type = "two.sided"
)

Arguments

x, q

vector of quantiles.

mean

mean

sd

standard deviation.

steps

vector of steps for the weight function.

omega

vector of weights defining the probability of observing a t-statistics between each of the two steps.

crit_x

vector of critical values defining steps (if steps are not supplied).

type

type of weight function (defaults to "two.sided").

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X \ge x]\).

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

Value

dwnorm gives the density, dwnorm gives the distribution function, qwnorm gives the quantile function, and rwnorm generates random deviates.

Details

The mean, sd, steps, omega can be supplied as a vectors (mean, sd) or matrices (steps, omega) with length / number of rows equal to x/q/ p. Otherwise, they are recycled to the length of the result.

See also

Normal

Examples

# generate random samples from weighted normal distribution
samples <- rwnorm(n = 10000, mean = 0.15, sd = 0.10,
                  steps = c(0.025, 0.5), omega = c(0.1, 0.5, 1),
                  type = "one.sided")
# hist(samples)

# compute density at specific values
density_vals <- dwnorm(x = c(-2, 0, 2), mean = 0, sd = 1,
                       steps = c(0.05), omega = c(0.5, 1))

# compute cumulative probabilities
prob_vals <- pwnorm(q = c(-1, 0, 1), mean = 0, sd = 1,
                    steps = c(0.05), omega = c(0.5, 1))