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

 hyperbCvMTest R Documentation

Cramer-von~Mises Test of a Hyperbolic Distribution

Description

Carry out a Cr<e4>mer-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, 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 Crmer-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 Cr<e4>mer-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 Cr<e4>mer-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”.

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 “Crmer-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)
```

HyperbolicDist documentation built on March 18, 2022, 6:23 p.m.