Title: Goodness-of-Fit Tests for Univariate Data via Energy
Version: 0.1
Description: Conduct one- and two-sample goodness-of-fit tests for univariate data. In the one-sample case, normal, uniform, exponential, Bernoulli, binomial, geometric, beta, Poisson, lognormal, Laplace, asymmetric Laplace, inverse Gaussian, half-normal, chi-squared, gamma, F, Weibull, Cauchy, and Pareto distributions are supported. egof.test() can also test goodness-of-fit to any distribution with a continuous distribution function. A subset of the available distributions can be tested for the composite goodness-of-fit hypothesis, that is, one can test for distribution fit with unknown parameters. P-values are calculated via parametric bootstrap.
License: GPL (≥ 3)
Encoding: UTF-8
Imports: energy, gsl, boot, fitdistrplus, statmod
URL: https://github.com/jthaman/energyGOF
RoxygenNote: 7.3.3
Suggests: testthat (≥ 3.0.0)
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2025-11-25 19:44:35 UTC; john
Author: John Haman [aut, cre]
Maintainer: John Haman <mail@johnhaman.org>
Repository: CRAN
Date/Publication: 2025-12-01 14:40:15 UTC

energyGOF: Goodness-of-Fit Tests via the Energy of Data

Description

Conduct one- and two-sample goodness-of-fit tests for univariate data. In the one-sample case, normal, uniform, exponential, Bernoulli, binomial, geometric, beta, Poisson, lognormal, Laplace, asymmetric Laplace, inverse Gaussian, half-normal, chi-squared, gamma, F, Weibull, Cauchy, and Pareto distributions are supported. egof.test() can also test goodness-of-fit to any distribution with a continuous distribution function. A subset of the available distributions can be tested for the composite goodness-of-fit hypothesis, that is, one can test for distribution fit with unknown parameters. P-values are calculated via parametric bootstrap.

Getting Started

The main entry point is energyGOF.test(). The only documentation you need to read is energyGOF.test() and energyGOF-package.

Here is a simple example to get you going 

x <- rnorm(10)

## Composite energy goodness-of-fit test (test for Normality with unknown
## parameters)

energyGOF.test(x, "normal", nsim = 1e5)

## Simple energy goodness-of-fit test (test for Normality with known
## parameters). egof.test is an alias for energyGOF.test.

egof.test(x, "normal", nsim = 1e5, mean = 0, sd = 1)


## Two-sample test
y <- rt(10, 1)
egof.test(x, y, nsim = 1e5)

## Test agaist any distribution function by transforming data to uniform
egof.test(y, pt, nsim = 1e5)

You may alternatively use the energyGOFdist() function, which is a different interface using S3 objects, but it provides the same result. There is a lot of documentation in this package for the various S3 constructors that are needed by energyGOFdist(), BUT if you just want to do some testing and use the standard interface, you can probably ignore all of that and just read the page for energyGOF.test().

Distributions Supported

The following distributions are supported.

Distribution Function Parameters Composite_Test
Asymmetric Laplace alaplace_dist location, scale, skew TRUE
Asymmetric Laplace asymmetric_laplace_dist location, scale, skew TRUE
Bernoulli bernoulli_dist prob FALSE
Beta beta_dist shape1, shape2 TRUE
Binomial binomial_dist size, prob FALSE
Cauchy cauchy_dist location, scale, pow TRUE
Chi-Squared chisq_dist df FALSE
Exponential exp_dist rate TRUE
Exponential exponential_dist rate TRUE
F f_dist df1, df2 FALSE
Gamma gamma_dist shape, rate FALSE
Geometric geometric_dist prob FALSE
Half-Normal halfnormal_dist scale TRUE
Inverse Gaussian inverse_gaussian_dist mean, shape TRUE
Inverse Gaussian invgauss_dist mean, shape TRUE
Laplace laplace_dist location, scale TRUE
Lognormal lognormal_dist meanlog, sdlog TRUE
Normal normal_dist mean, sd TRUE
Pareto (Type I) pareto_dist scale, shape, pow TRUE
Poisson poisson_dist lambda TRUE
Uniform uniform_dist min, max FALSE
Weibull weibull_dist shape, scale TRUE

Simple and Composite Testing

There are two types of goodness-of-fit tests covered by the energyGOF package, simple and composite. It's important to know the difference because they yield different results. Simple GOF tests test the data x against a specific distribution with known parameters that you must pass to energyGOF.test in the ellipsis argument (...). You should use a simple GOF test if you wish to test questions like "my data are Normal with mean 1 and sd 2". energyGOF() can also conduct some composite GOF tests. A composite test is performed if no parameters are passed in the ellipsis argument (...). You should conduct a composite test if your research question is "my data are Normal, but I don't know what the parameters are." Obviously, this composite question is much more common in practice.

All the composite tests in energyGOF assume that none of the parameters are known. So while there is a statistical test of Normality with known mean and unknown sd, this is not implemented in the energyGOF package. So, either pass all the distribution parameters or none of them. (In the special case of the Normal distribution, you can use the energy::energy package to test the GOF hypothesis with any combination of known and unknown parameters.)

For each test, energyGOF.test() calculates the test statistic and a p-value. In all cases the p-value is calculated via parametric bootstrap. For large nsim, the p-values should be reasonably honest in small-ish samples. You may need to perform a sensitivity study to find a reasonable nsim for your particular testing problem.

Power Analyses

Please see the repository https://github.com/jthaman/energyGOF-power for examples of how to conduct power analyses with energyGOF, and for preliminary performance data agaist alternative methods.

About Energy

Székely, G. J., & Rizzo, M. L. (2023) provide the motivation:

"Data energy is a real number (typically a non-negative number) that depends on the distances between data. This concept is based on the notion of Newton’s gravitational potential energy, which is also a function of the distance between bodies. The idea of data energy or energy statistics is to consider statistical observations (data) as heavenly bodies governed by the potential energy of data, which is zero if and only if an underlying statistical hypothesis is true."

The notation X' indicates that X' is an independent and identically distributed copy of X.

If X and Y are independent and E(|X|^s + |Y|^s) is finite, then for 0 < s < 2,

2E|X-Y|^s - E|X-X'|^s - E|Y-Y'|^s \ge 0.

Equality is attained if and only if X and Y are identically distributed. The left side of the equation is the energy between X and Y. Energy can be generalized to multivariate data and even more exotic data types, but in this R package, we only treat univariate data.

The concept of data energy between two random variables can be adapted to the one-sample goodness-of-fit problem. The one-sample s-energy is

E^* = \frac{2}{n} \sum_i E|x_i - Y|^s - E|Y-Y'|^s - \frac{1}{n^2} \sum_i \sum_j |x_i - x_j|^s,

when 0 < s < 2 and E|X|^s, E|Y|^s < \infty.

In most tests in the energyGOF package s = 1. In some cases (Pareto and Cauchy), E|Y| is not finite, so we need to use an s < 1. This is done by passing pow into ... (but in all tests a default pow is provided). These tests are called generalized energy goodness-of-fit tests in this package as well as in Székely, G. J., & Rizzo, M. L. (2023).

To connect energy back to GOF testing, in the one-sample goodness-of-fit regime, we test if a sample x_1, \ldots, x_n \sim X (where the distribution of X is hidden) follows the same distribution as Y, which is specified. If X and Y have the same distribution, then the distribution of Q = nE^* is a quadratic form of centered Gaussian random variables with expected value E|Y-Y'|^s. If X and Y differ, then Q \to \infty with n. So, Q provides a consistent goodness-of-fit test, even in some situations where E|Y| is not finite. Asymptotic theory of V-statistics can be applied to prove that tests based on Q are statistically consistent goodness-of-fit tests.

Author(s)

John T. Haman

References

Székely, G. J., & Rizzo, M. L. (2023). The energy of data and distance correlation. Chapman and Hall/CRC.

Székely, G. J., & Rizzo, M. L. (2013). Energy statistics: A class of statistics based on distances. Journal of statistical planning and inference, 143(8), 1249-1272.

Li, Y. (2015). Goodness-of-fit tests for Dirichlet distributions with applications. Bowling Green State University.

Rizzo, M. L. (2002). A new rotation invariant goodness-of-fit test (PhD thesis). Bowling Green State University

Haman, J. T. (2018). The energy goodness-of-fit test and EM type estimator for asymmetric Laplace distributions (Doctoral dissertation, Bowling Green State University).

Ofosuhene, P. (2020). The energy goodness-of-fit test for the inverse Gaussian distribution (Doctoral dissertation, Bowling Green State University).

Rizzo, M. L. (2009). New goodness-of-fit tests for Pareto distributions. ASTIN Bulletin: The Journal of the IAA, 39(2), 691-715.

Yang, G. (2012). The Energy Goodness-of-fit Test for Univariate Stable Distributions (Doctoral dissertation, Bowling Green State University).

See Also

Useful links:

Create an asymmetric Laplace 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 an asymmetric Laplace distribution. If all three parameters are NULL, perform a composite test. This is exactly the distribution corresponding to the PDF

f(x | \theta, \sigma, \kappa) = \frac{\sqrt{2}\kappa}{\sigma(1 + \kappa^2)} \begin{cases} \exp\Big( -\frac{\sqrt{2} \kappa |x - \theta|}{\sigma} \Big), & x \ge \theta, \\[6pt] \exp\Big( -\frac{\sqrt{2} |x - \theta|}{\kappa \sigma} \Big), & x < \theta. \end{cases} ,

where \theta = location, \sigma = scale, and \kappa = skew.

Usage

asymmetric_laplace_dist(location = NULL, scale = NULL, skew = NULL)

alaplace_dist(location = NULL, scale = NULL, skew = NULL)

Arguments

location

NULL, or a location parameter

scale

NULL, or a positive scale parameter

skew

NULL, or a positive skewness parameter. Skew = 1 corresponds to a symmetric Laplace distribution (though note the difference between the PDF in this description and the one in laplace_dist()).

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples


d <- asymmetric_laplace_dist(0, 1, .5)
x <- d$sampler(10, d$par)

egofd(x, d, 0)

Create a Bernoulli 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 Bernoulli distribution. Only simple tests are implemented.

Usage

bernoulli_dist(prob = 0.5)

Arguments

prob

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

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples


d <- bernoulli_dist(.5)
egofd(rbinom(10, 1, .5), d, 0)

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)

Arguments

shape1

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

shape2

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

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples

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

Create a Binomial 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 Binomial distribution. Only a simple GOF test is supported.

Usage

binomial_dist(size = 1, prob = 0.5)

Arguments

size

Same as stats::rbinom(), but must be length 1.

prob

Same as stats::rbinom(), but must be length 1.

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples


d <- binomial_dist(1, 0.5)
egofd(rbinom(10, 1, .5), d, 0)

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)

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.

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples

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

Create a Chi-squared 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 Chi-squared distribution. Only simple tests are supported.

Usage

chisq_dist(df = 2)

Arguments

df

Same as in stats::rchisq().

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples

d <- chisq_dist(4)
egofd(rchisq(10, 4), d, 0)

Goodness-of-fit tests for univariate data via energy

Description

Perform a goodness-of-fit test of univariate data x against a target y. y may be one of the following:

P-values are determined via parametric bootstrap. For distributions where E|Y| is not finite (Cauchy, Pareto), a generalized energy goodness-of-fit test is performed, and an additional tuning parameter pow is required.

Usage

energyGOF.test(x, y, nsim, ...)

egof.test(x, y, nsim, ...)

Arguments

x

A numeric vector.

y

A string, distribution function, or numeric vector. The distribution to test x against.

nsim

A non-negative integer. The number of parametric bootstrap replicates taken to calculate the p-value. If 0, no simulation.

...

If y is a string or distribution function, parameters of the distribution y. Required for a simple test. For distributions in the stats library, parameter argument names are identical. If y is a string, to test the composite goodness-of-fit hypothesis that x is distributed according to the family of distributions y, don't pass parameters in .... For generalized energy tests, you can also optionally pass the generalized energy exponent pow here. Composite testing is not supported if y is a function. (As you can see, there is a lot going on in ... and if you don't like that, you may want to check out energyGOFdist() for a structured interface.)

Value

If y is a string or function, return an object of class ‘htest’ representing the result of the energy goodness-of-fit hypothesis test. The htest object has the elements:

If y is numeric, return the same htest object as energy::eqdist.etest().

Author(s)

John T. Haman

See Also

Examples

x <- rnorm(10)
y <- rt(10, 4)

## Composite energy goodness-of-fit test (test for Normality with unknown
## parameters)

energyGOF.test(x, "normal", nsim = 10)

## Simple energy goodness-of-fit test (test for Normality with known
## parameters). egof.test is an alias for energyGOF.test.

egof.test(x, "normal", nsim = 10, mean = 0, sd = 1)

## Alternatively, use the energyGOFdist generic directly so that you do not need
## to pass parameter names into `...`

energyGOFdist(x, normal_dist(0, 1), nsim = 10)

## Conduct a two-sample test

egof.test(x, y, 0)

## Conduct a test against any continuous distribution function

egof.test(x, pcauchy, 0)

## Simple energy goodness-of-fit test for Weibull distribution

y <- rweibull(10, 1, 1)
energyGOF.test(y, "weibull", shape = 1, scale = 3, nsim = 10)

## Alternatively, use the energyGOFdist generic directly, which is slightly less
## verbose. egofd is an alias for energyGOFdist.

egofd(y, weibull_dist(1, 3), nsim = 10)

## Conduct a generalized GOF test. `pow` is the exponent *s* in the generalized
## energy statistic. Pow is only necessary when testing Cauchy, and
## Pareto distributions. If you don't set a pow, there is a default for each
## of the distributions, but the default isn't necessarily better than any
## other number.

egofd(rcauchy(100),
   cauchy_dist(location = 0, scale = 1, pow = 0.5),
   nsim = 10)

## energyGOF does not support tests with a mix of known and unknown
## parameters, so this will result in an error.


  energyGOF.test(x, "normal", mean = 0, nsim = 10) # sd is missing

S3 Interface to Parametric Goodness-of-Fit Tests via Energy

Description

This is an alternative interface that provides the same parametric tests as energyGOF.test(), but allows the user to directly pass a distribution object like normal_dist() (Distribution objects are specific to the implementation of this R package). The advantage is that you do not need to pass distribution parameters into a ... argument as in energyGOF.test(). energyGOF.test() uses this function under the hood, but it's perfectly suitable for the user to use as well.

Usage

energyGOFdist(x, dist, nsim)

egofd(x, dist, nsim)

Arguments

x

A numeric vector.

dist

An object of class GOFDist. The distribution to test x against. GOFDist objects are created with the various "*_dist()" functions in this package. See, for example, normal_dist() for details on these class objects.

nsim

A non-negative integer. The number of parametric bootstrap replicates taken to calculate the p-value. If 0, no simulation.

Value

Return an object of class ‘htest’ representing the result of the energy goodness-of-fit hypothesis test. The htest object has the elements:

Author(s)

John T. Haman

Examples

## Simple normal test
energyGOFdist(rnorm(10), normal_dist(0, 1), nsim = 10)

## Simple Poisson test
egofd(rpois(10,1), poisson_dist(1), nsim = 0) # No p-value

## Composite Normal test
egofd(rnorm(10), normal_dist(), nsim = 10)

Create an Exponential 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 an exponential distribution. If rate is NULL, a composite test is performed.

Usage

exponential_dist(rate = NULL)

Arguments

rate

NULL, or a positive rate parameter as in rexp(), but must be length 1.

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples


d <- exponential_dist(1)
egofd(rexp(10, 1), d, 0)

Create an F 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 F distribution. Only simple tests are supported.

Usage

f_dist(df1 = 3, df2 = 3)

Arguments

df1

Positive.

df2

Must be greater than 2.

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples


d <- f_dist(3, 3)
egofd(rf(10, 3, 3), d, 0)

Create a gamma 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 Gamma distribution. Only simple tests are supported.

Usage

gamma_dist(shape = 1, rate = 1)

Arguments

shape

Same shape parameter in stats::rgamma() (must be length 1)

rate

Same rate parameter in stats::rgamma() (must be length 1)

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples

d <- gamma_dist(4, 4)
egofd(rgamma(10, 4, 4), d, 0)

Create a geometric 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 geometric distribution. Only a simple test is supported.

Usage

geometric_dist(prob = 0.5)

Arguments

prob

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

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples


d <- geometric_dist(.5)
egofd(rgeom(10, .5), d, 0)

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)

Arguments

scale

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

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples


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

Create an inverse Gaussian 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 an inverse Gaussian distribution. If mean and shape are both NULL, perform a composite test. This is exactly the distribution corresponding to the PDF

f(x | \mu, \lambda) = \left( \frac{\lambda}{2 \pi x^3} \right)^{1/2} \exp \left( -\frac{\lambda (x - \mu)^2}{2 \mu^2 x} \right), \qquad x > 0,

where mean is \mu and shape is \lambda.

Usage

inverse_gaussian_dist(mean = NULL, shape = NULL)

invgauss_dist(mean = NULL, shape = NULL)

Arguments

mean

NULL or a positive mean parameter

shape

NULL or a positive shape parameter

Details

This distribution requires an intense amount of numerical integration for the simple (known parameters) case, and the implementation seems to be fine for samples up to 1000. For the composite case, the data are transformed to a Chi-squared distribution (conditional on the parameter estimates), and the performance is much better, as there is no numerical integration in this case.

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples

d <- inverse_gaussian_dist(4, 4)
x <- d$sampler(10, d$par)

egofd(x, d, 0)

Create a Laplace 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 Laplace distribution. If location and scale are both NULL, a composite test is performed.

This is exactly the distribution corresponding to the PDF

f(x|\mu, b) = \frac{1}{2b} \exp \left(-\frac{|x - \mu|}{b} \right),

where location = \mu and scale = b.

Usage

laplace_dist(location = NULL, scale = NULL)

Arguments

location

NULL, or the median of the distribution

scale

NULL or a positive scale parameter

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples

d <- laplace_dist(1, 1)

x <- d$sampler(10, d$par)

egofd(x, d, 0)

Create a lognormal 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 lognormal distribution. If meanlog and sdlog are both NULL, a composite test is performed.

Usage

lognormal_dist(meanlog = NULL, sdlog = NULL)

Arguments

meanlog

NULL or as in rlnorm(), must be length 1.

sdlog

NULL or as in rlnorm(), must be length 1.

d <- lognormal_dist(0, 1) x <- d$sampler(10, d$par)

egofd(x, d, 0)

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Create a 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 normal distribution. If mean and sd are both NULL, perform a composite test.

Usage

normal_dist(mean = NULL, sd = NULL)

Arguments

mean

NULL, or if specified, same as rnorm(), but must be length 1.

sd

NULL, or if specified, Same as rnorm(), but must be length 1

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples

d <- normal_dist(0, 1)

# Composite test
dc <- normal_dist()
egofd(rnorm(10), dc, 0)


### Expected distances:

d$EYY(d$par)

## should be about the same as mean(abs(rnorm(1e5) - rnorm(1e5)))

x <- 3

d$EXYhat(3, d$par)

## should be about the same as mean(abs(x - rnorm(1e5)))

Create a Pareto (type I) 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 Pareto distribution. If scale and shape are both NULL, perform a composite test.

Usage

pareto_dist(scale = NULL, shape = NULL, pow = NULL)

Arguments

scale

NULL or a positive scale parameter

shape

NULL or a positive shape parameter. If shape > 1, shape is used to transform x

pow

Optional exponent of the energy test. Pow must be less than shape. If shape > 1 and pow != 1, pow will be scaled down.

Details

If shape > 1, the energy test is more difficult, so data are transformed to data^shape ~ Pareto(scale^shape, 1).

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples

d <- pareto_dist(1, .5)
x <- d$sampler(10, d$par)
egofd(x, d, 0)

Create a Poisson 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 Poisson distribution. If lambda is NULL, a composite test is performed.

Usage

poisson_dist(lambda = NULL)

Arguments

lambda

NULL, or if specified, same as the lambda in rpois(), but must be length 1.

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples

d <- poisson_dist(1)

egofd(rpois(10, 1), d, 0)

Create a Uniform 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 uniform distribution. Only simple tests are implemented.

Usage

uniform_dist(min = 0, max = 1)

Arguments

min

Same as in runif(), but must be length 1

max

Same as in runif(), but must be length 1

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples


d <- uniform_dist(0, 1)

egofd(runif(10), d, 0)

Create a Weibull distribution object for energy testing

Description

Create a Weibull distribution object for energy testing

Usage

weibull_dist(shape = NULL, scale = NULL)

Arguments

shape

NULL, or if specified, same as the shape parameter in stats::rweibull()

scale

NULL, or if specified, same as the scale parameter in stats::rweibull() #' @description Create an S3 object that sets all the required data needed by energyGOFdist to execute the energy goodness-of-fit test against a Weibull distribution. If shape and scale are both NULL, perform a composite test.

Value

S3 data object containing the following fields.

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.

Author(s)

John T. Haman

Examples


d <- weibull_dist(3, 3)
egofd(rweibull(10, 3, 3), d, 0)