hyperbCvMTest function

Cramer-von~Mises Test of a Hyperbolic Distribution

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

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 class 'hyperbCvMTest'
print(x, prefix = "\t", ...)

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 -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.

Details

hyperbCvMTest carries out a -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 -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 .

Returns

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.

Author(s)

David Scott, Thomas Tran

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

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)