Null Distribution of Anderson-Darling Test Statistic

pAD computes the cumulative distribution function, and qAD computes the quantile function, of the null distribution of the Anderson-Darling test statistic.

Usage

pAD(q, n = Inf, lower.tail = TRUE, fast = TRUE)

qAD(p, n = Inf, lower.tail = TRUE, fast = TRUE)

Arguments

q: Numeric vector of quantiles (values for which the cumulative probability is required).
n: Integer. Sample size for the Anderson-Darling test.
lower.tail: Logical. If TRUE (the default), probabilities are \(P(X \le q)\), and otherwise they are \(P(X > q)\).
fast: Logical value indicating whether to use a fast algorithm or a slower, more accurate algorithm, in the case n=Inf.
p: Numeric vector of probabilities.

Value

A numeric vector of the same length as p or q.

Details

pAD uses the algorithms and C code described in Marsaglia and Marsaglia (2004).

qAD uses uniroot() to find the quantiles.

The argument fast applies only when n=Inf and determines whether the asymptotic distribution is approximated using the faster algorithm adinf (accurate to 4-5 places) or the slower algorithm ADinf (accurate to 11 places) described in Marsaglia and Marsaglia (2004).

Note

Original C code by G. and J. Marsaglia. R interface by Adrian Baddeley, adapted to conform to package standards.

References

Anderson, T.W. and Darling, D.A. (1952) Asymptotic theory of certain 'goodness-of-fit' criteria based on stochastic processes. Annals of Mathematical Statistics 23, 193–212.

Anderson, T.W. and Darling, D.A. (1954) A test of goodness of fit. Journal of the American Statistical Association 49, 765–769.

Marsaglia, G. and Marsaglia, J. (2004) Evaluating the Anderson-Darling Distribution. Journal of Statistical Software 9 (2), 1–5. February 2004. http://www.jstatsoft.org/v09/i02

Examples


  pAD(1.1, n=5)
#> [1] 0.6945818
  pAD(1.1)
#> [1] 0.6911871
  pAD(1.1, fast=FALSE)
#> [1] 0.6912038

  qAD(0.5, n=5)
#> [1] 0.7640094
  qAD(0.5)
#> [1] 0.7742347