approx: Distribution Approximations

In exams.forge: Support for Compiling Examination Tasks using the 'exams' Package

Distribution Approximations

Description

These functions check whether a normal approximation is appropriate for a given distribution. They return TRUE if the approximation condition is met, and FALSE otherwise. The threshold parameter c can be set directly or retrieved via getOption().

The functions apply the following rules:

• t2norm: n > c with default c = 30.

• binom2norm:

  • If type = "single" (default), the approximation is valid if ⁠size × prob × (1 - prob) > c⁠.

  • If type = "double", the approximation requires both ⁠size × prob > c⁠ and ⁠size × (1 - prob) > c⁠, with default c = 9.

• clt2norm: n > c with default c = 30. Note that the existence of expectation and variance, required by the Central Limit Theorem, cannot be checked automatically.

Usage

t2norm(n, c = getOption("distribution.t2norm", 30))

binom2norm(
  size,
  prob,
  c = getOption("distribution.binom2norm", 9),
  type = c("single", "double")
)

clt2norm(n, c = getOption("distribution.clt2norm", 30))

approx_binom2norm(
  size,
  prob,
  c = getOption("distribution.binom2norm", 9),
  type = c("single", "double")
)

approx_clt2norm(n, c = getOption("distribution.clt2norm", 30))

approx_t2norm(n, c = getOption("distribution.t2norm", 30))

Arguments

n	integer: number of observations (for t2norm and clt2norm)
c	numeric: threshold parameter for approximation (default via getOption() or a default value)
size	integer: number of trials (for binom2norm)
prob	numeric: probability of success on each trial (for binom2norm)
type	character: approximation type, "single" or "double" (for binom2norm)

Value

logical: TRUE if the approximation is valid, FALSE otherwise

Examples

# Check for 5 and 50 observations
t2norm(n = c(5, 50))
binom2norm(size = c(5, 50), prob = 0.5)
binom2norm(size = c(5, 50), prob = 0.5, type = "double")

exams.forge documentation built on Aug. 21, 2025, 5:41 p.m.