energyGOF (version 0.1)

cauchy_dist: Create a Cauchy distribution object for energy testing

Description

Create an S3 object that sets all the required data needed by energyGOFdist to execute the generalized energy goodness-of-fit test against a Cauchy distribution. If location and scale are both NULL, perform a composite test.

Usage

cauchy_dist(location = NULL, scale = NULL, pow = 0.5)

Value

S3 data object containing the following fields.

• name: String

• composite_p: Composite predicate. TRUE if test is composite.

• par: Distribution parameters, list of the formals.

• sampler_par: Distribution parameters used for the calculation of energy statistic. These may be different than par.

• par_domain: Function used to ensure par and sampler_par are valid for this distribution

• support: Function to check that data x can be tested against y

• sampler: Function used for rng by boot::boot()

• EYY: Function to compute \(E|Y-Y'|\) (or \(E|Y-Y'|^{pow}\), for the generalized test.)

• EXYhat: Function to compute \(\frac{1}{n} \sum_i E|x_i - Y|\) (or \(\frac{1}{n} \sum_i E|x_i - Y|^{pow}\)), where Y is distributed according to y and x is the data under test (which is passed in egof.test or egofd).

• xform: Function that may be used to transform x. Only available in certain distribution objects.

• statistic: Function that returns a list of maximum likelihood estimates. Only available in certain distribution objects.

• notes: Distribution specific messages. Only used in certain distribution objects.

Note: Some distributions do not have notes, xform, and statistic fields. This is because either a composite test is not implemented, or because a data transformation is not needed.

Arguments

location

NULL, or same as in stats::rcauchy()

scale

NULL, or same as in stats::rcauchy()

pow

Optionally set the exponent of the energy test. 0 < pow < 1 is required for the Cauchy distribution. Default is 0.5.

Author

John T. Haman

Examples

d <- cauchy_dist(4, 4)
x <- rcauchy(10, 4, 4)
egofd(x, d, 0)