energyGOF (version 0.1)

halfnormal_dist: Create a half-normal 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 half-normal distribution. If scale is NULL, a composite test is performed.

This is exactly the distribution of \(|X|\), where \(X ~ N(0,\theta = scale)\)

Usage

halfnormal_dist(scale = 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

scale

NULL, or a positive scale parameter, like sd in rnorm(). Must be length 1.

Author

John T. Haman

Examples

d <- halfnormal_dist(4)
egofd(abs(rnorm(10, 4)), d, 0)