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Cramer-von Mises Normality Test

Source: R/Cramer_von_Mises_test.R
Cramer_von_Mises_test.Rd

An empirical distribution function (EDF)-based goodness-of-fit test that measures the overall discrepancy between the empirical and theoretical cumulative distribution functions by assigning relatively uniform weight across the entire distribution.

Usage

Cramer_von_Mises_test(
  x,
  alpha = 0.05,
  silent = FALSE,
  summary = TRUE,
  misc = FALSE
)

Arguments

x

A numeric vector, at least length of 8.

alpha

Numeric (default: 0.05). Significance threshold, range from 0 to 1.

silent

Logical (default: FALSE). If FALSE, print out the results.

summary

Logical (default: TRUE). Produce a summary table.

misc

Logical (default: FALSE). Output other unimportant parameters.

Value

A list.

References

Thode, H. C., Jr., 2002. Goodness of fit tests. Testing for normality. Marcel Dekker, New York. (Section 5.1.3, pg. 103)

Stephens, M.A., 2017. Tests Based on EDF Statistics. In: D'Agostino, R.B., Stephens, M.A. (Eds.), Goodness-of-Fit Techniques, 1st ed. Routledge, New York, (Table 4.9, pg. 127). https://doi.org/10.1201/9780203753064

Examples

out <- Cramer_von_Mises_test(rnorm(10))
#> 
#> ------------------------------------
#> Cramer-von-Mises (W2) normality test 
#> 
#> Statistic (W2) = 0.0311 
#> p-value = 0.80906
#> ------------------------------------
print(out$summary)
#>                       alpha  statistic      pval signif standard_value
#> Cramer-von-Mises (W2)  0.05 0.03109938 0.8090619     ns     0.03265434
#>                       critical_value SE CI_lower CI_upper  N        AVG
#> Cramer-von-Mises (W2)             NA NA       NA       NA 10 -0.1786959
#>                              MED       MIN      MAX      SD
#> Cramer-von-Mises (W2) -0.2873072 -1.863011 2.065025 1.17598