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, Theta, conf.level = 0.95, ...)
hyperbCvMTestPValue(xi, chi, 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.

• Theta: Parameters of the hyperbolic distribution taking the form c(pi,zeta,delta,mu).

• conf.level: Confidence level of the the confidence interval.

• ...: Further arguments to be passed to or from methods.

• xi: Value of $xi$ in the $(xi,chi)$

  parameterization of the hyperbolic distribution.

• chi: Value of $chi$ in the $(xi,chi)$

  parameterisation of the hyperbolic distribution.

• 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 Theta must be given in the $(pi,zeta)$

parameterisation.

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 HyperbolicDist 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 Crämer-von~Mises test of hyperbolic distribution .

• data.name: A character string giving the name(s) of the data.

• parameter: The value of the parameter Theta.

• 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

Theta <- c(2,2,2,2)
dataVector <- rhyperb(500, Theta)
fittedTheta <- hyperbFit(dataVector)$Theta
hyperbCvMTest(dataVector, fittedTheta)
dataVector <- rnorm(1000)
fittedTheta <- hyperbFit(dataVector, startValues = "FN")$Theta
hyperbCvMTest(dataVector, fittedTheta)