gibb_entropy: Gibbs entropy of Generalized Gamma Distribution

In genomaths/MethylIT: Methylation Analysis Based on Signal Detection

Gibbs entropy of Generalized Gamma Distribution

Description

This function computes the Gibbs entropy for member of the Generalized Gamma (GG) Distribution family. GG density is given as:

exp(-y^\alpha) * \alpha*y^(\alpha*\delta - 1)/(scale*\gamma(\delta))

(see (Wikipedia))

A list of the member of the GG distribution family with the corresponding parameter settings is provided in Table 1 from reference (1). For example, to compute the Gibbs entropy of a Weibull distribution model, we just set: alpha > 0 and delta = 1 (notice that parameter are named different in reference (1)).

Usage

gibb_entropy(model, R = 8.31446261815324, ...)

## S4 method for signature 'missingORNULL'
gibb_entropy(
  model,
  R = 8.31446261815324,
  pars,
  log.base = exp(1),
  terms = FALSE
)

## S4 method for signature 'cdfMODEL'
gibb_entropy(model, R = 8.31446261815324, log.base = exp(1), terms = FALSE)

## S4 method for signature 'cdfMODELlist'
gibb_entropy(model, R = 8.31446261815324, log.base = exp(1), terms = FALSE)

## S4 method for signature 'ProbDistrList'
gibb_entropy(model, R = 8.31446261815324, log.base = exp(1), terms = FALSE)

Arguments

model	An object from any of the classes created in MethylIT pipeline: cdfMODEL, cdfMODELlist, or ProbDistrList. If given, then the parameter values are taken from the model.
R	A number or NULL. The gas constant (R = 8.31446261815324 J * (K * mol)^-1) is given as default value, which is proportionality constant that relates the energy scale in physics to the temperature scale and the scale used for amount of substance.
pars	Optional. A numerical vector containing the model parameter values in the given in order: alpha, scale, and delta.
log.base	A positive number. The same as in function log.
terms	logical(1). If term = TRUE, then a numerical vector with terms contributing to the Gibb entropy are provided.

Details

The value of the constant R can be simply 1, which returns the Shannon entropy in bit units, only carrying informational meaning.

Value

Gibb entropy of the model. Shannon entropy is returned by setting R = 1 and log.base = 2.

References

1. Crooks, Gavin E. (2015) The Amoroso Distribution. arXiv:1005.3274v2.

See Also

helmholtz_free_energy

Examples

## Loading the probability distribution models
data(gof, "MethylIT")
## Gibb entropy in J * (K * mol)^-1)
gibb_entropy(gof)

genomaths/MethylIT documentation built on Feb. 3, 2024, 1:24 a.m.