goftest (version 1.0-1)

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 latex{Cram'er}{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 latex{Cram'er}{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 latex{Cs"org"o}{Csorgo} and Faraway (1996).

qCvM uses uniroot to find the quantiles.

References

latex{Cs"orgo}{Csorgo}, S. and Faraway, J.J. (1996) The exact and asymptotic distributions of latex{Cram'er}{Cramer}-von Mises statistics. Journal of the Royal Statistical Society, Series B 58, 221--234.

See Also

cvm.test

Examples

Run this code
pCvM(1.1, n=5)
  pCvM(1.1)

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

Run the code above in your browser using DataCamp Workspace