goftest (version 1.2-3)

pCvM: Null Distribution of Cramer-von Mises Test Statistic

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

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 \(P(X \le q)\), and otherwise they are \(P(X > q)\).

Value

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

Details

For finite n the cumulative distribution function is approximated by the first order expansion \(V(x) + \psi_1(x)/n\), equation (1.8) of Csorgo and Faraway (1996).

qCvM uses uniroot to find the quantiles.

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

# NOT RUN {
  pCvM(1.1, n=5)
  pCvM(1.1)

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