Dogoftest (version 0.3)

CVMgof2: One-Sample Cramér–von Mises Goodness-of-Fit Test

Description

Performs the one-sample Cramér–von Mises goodness-of-fit (GoF) test to assess whether a sample comes from a specified distribution using asymptotic p-value approximations.

Usage

CVMgof2(
  x,
  dist = c("norm", "exp", "unif", "lnorm", "weibull", "gamma", "t", "chisq"),
  ...,
  eps = 1e-15
)

Value

An object of class "htest" with the following components:

statistic

The computed Cramér–von Mises test statistic.

p.value

The asymptotic p-value.

method

A description of the test and distribution.

data.name

The name of the data vector.

Arguments

x

A numeric vector of observations.

dist

A character string specifying the theoretical distribution. Must be one of "norm", "exp", "unif", "lnorm", "weibull", "gamma", "t", or "chisq".

...

Distribution parameters passed to the corresponding p functions (e.g., mean, sd, rate, df, etc.).

eps

A small value to truncate extreme p-values (default is 1e-15).

Details

The test uses the Cramér–von Mises statistic to assess how well the empirical distribution function (EDF) of the sample agrees with the cumulative distribution function (CDF) of the specified theoretical distribution. The p-value is computed using approximation formulas derived from the asymptotic distribution of the test statistic.

Examples

set.seed(123)
x1 <- rnorm(500, mean = 0, sd = 1)
CVMgof2(x1, dist = "norm", mean = 0, sd = 1)

x2 <- rexp(500, rate = 2)
CVMgof2(x2, dist = "exp", rate = 2)

x3 <- runif(200, min = -1, max = 3)
CVMgof2(x3, dist = "unif", min = -1, max = 3)