R: Null Distribution of Cramer-von Mises Test Statistic

pCvM {goftest} | R Documentation

## 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 <= 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

      pCvM(1.1, n=5)
      pCvM(1.1)

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

[Package goftest version 1.2-2 Index]