pCvM: Null Distribution of Cramer-von Mises Test Statistic

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

pCvM computes the cumulative distribution function, and qCvM computes the quantile function, of the null distribution of the Cramer-von Mises test statistic.

Usage

1
2
  pCvM(q, n = Inf, lower.tail = TRUE)
  qCvM(p, n = Inf, lower.tail = TRUE)

Arguments

q

Numeric vector of quantiles (values for which the cumulative probability is required).

p

Numeric vector of probabilities.

n

Integer. Sample size for the Cramer-von Mises test.

lower.tail

Logical. If TRUE (the default), probabilities are P(X <= q), and otherwise they are P(X > q).

Details

For finite n the cumulative distribution function is approximated by the first order expansion V(x) + psi1(x)/n, equation (1.8) of Csorgo and Faraway (1996).

qCvM uses uniroot to find the quantiles.

Value

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

Author(s)

Original Matlab code by Julian Faraway, translated to R by Adrian Baddeley.

References

Csorgo, S. and Faraway, J.J. (1996) The exact and asymptotic distributions of Cramer-von Mises statistics. Journal of the Royal Statistical Society, Series B 58, 221–234.

See Also

cvm.test

Examples

1
2
3
4
5
  pCvM(1.1, n=5)
  pCvM(1.1)

  qCvM(0.5, n=5)
  qCvM(0.5)

Example output

[1] 0.9996994
[1] 0.9985628
[1] 0.1224682
[1] 0.1188807

goftest documentation built on Oct. 7, 2021, 5:07 p.m.