energyGOF (version 0.1)

beta_dist: Create a beta distribution object for energy testing

Description

Create an S3 object that sets all the required data needed by energyGOFdist to execute the energy goodness-of-fit test against a beta distribution. If shape1 and shape2 are NULL, a composite test is performed, otherwise a simple test is performed.

Usage

beta_dist(shape1 = NULL, shape2 = NULL)

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

shape1

Same as rbeta(), but must be length 1.

shape2

Same as rbeta(), but must be length 1.

Author

John T. Haman

Examples

d <- beta_dist(5, 5)
egofd(rbeta(10, 5, 5), d, 0)