hyperbCvMTest: Cramer-von~Mises Test of a Hyperbolic Distribution

Description

Carry out a Cramér-von~Mises test of a hyperbolic distribution where the parameters of the distribution are estimated, or calculate the p-value for such a test.

Usage

hyperbCvMTest(x, mu = 0, delta = 1, alpha = 1, beta = 0,
              param = c(mu, delta, alpha, beta),
              conf.level = 0.95, ...)
hyperbCvMTestPValue(delta = 1, alpha = 1, beta = 0, Wsq, digits = 3)
# S3 method for hyperbCvMTest
print(x, prefix = "\t", ...)

Value

hyperbCvMTest returns a list with class hyperbCvMTest

containing the following components:

statistic: The value of the test statistic.
method: A character string with the value “Cramér-von~Mises test of hyperbolic distribution”.
data.name: A character string giving the name(s) of the data.
parameter: The value of the parameter param
p.value: The p-value of the test.
warn: A warning if the parameter values are outside the limits of the table given in Puig & Stephens (2001).

hyperbCvMTestPValue returns a list with the elements

p.value and warn only.

Arguments

x: A numeric vector of data values for hyperbCvMTest, or object of class "hyperbCvMTest" for print.hyperbCvMTest.
mu: \(\mu\) is the location parameter. By default this is set to 0.
delta: \(\delta\) is the scale parameter of the distribution. A default value of 1 has been set.
alpha: \(\alpha\) is the tail parameter, with a default value of 1.
beta: \(\beta\) is the skewness parameter, by default this is 0.
param: Parameters of the hyperbolic distribution taking the form c(mu, delta, alpha, beta).
conf.level: Confidence level of the the confidence interval.
...: Further arguments to be passed to or from methods.
Wsq: Value of the test statistic in the Cramér-von~Mises test of the hyperbolic distribution.
digits: Number of decimal places for p-value.
prefix: Character(s) to be printed before the description of the test.

Author

David Scott, Thomas Tran

Details

hyperbCvMTest carries out a Cramér-von~Mises goodness-of-fit test of the hyperbolic distribution. The parameter param must be given in the \((\alpha, \beta)\) parameterization.

hyperbCvMTestPValue calculates the p-value of the test, and is not expected to be called by the user. The method used is interpolation in Table 5 given in Puig & Stephens (2001), which assumes all the parameters of the distribution are unknown. Since the table used is limited, large p-values are simply given as “>~0.25” and very small ones as “<~0.01”. The table is created as the matrix wsqTable when the package GeneralizedHyperbolic is invoked.

print.hyperbCvMTest prints the output from the Cramér-von~Mises goodness-of-fit test for the hyperbolic distribution in very similar format to that provided by print.htest. The only reason for having a special print method is that p-values can be given as less than some value or greater than some value, such as “<\ ~0.01”, or “>\ ~0.25”.

References

Puig, Pedro and Stephens, Michael A. (2001), Goodness-of-fit tests for the hyperbolic distribution. The Canadian Journal of Statistics/La Revue Canadienne de Statistique, 29, 309--320.

Examples

Run this code

param <- c(2, 2, 2, 1.5)
dataVector <- rhyperb(500, param = param)
fittedparam <- hyperbFit(dataVector)$param
hyperbCvMTest(dataVector, param = fittedparam)
dataVector <- rnorm(1000)
fittedparam <- hyperbFit(dataVector, startValues = "FN")$param
hyperbCvMTest(dataVector, param = fittedparam)

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