Gibbs entropy of Generalized Gamma Distribution

Source: R/gibb_entropy.R

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)).

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

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

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

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

# S4 method for 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.

Value

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

Details

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

References

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

Examples

## Loading the probability distribution models
data(gof, "MethylIT")
#> Warning: data set ‘MethylIT’ not found
## Gibb entropy in J * (K * mol)^-1)
gibb_entropy(gof)
#>       C1       C2       C3       T1       T2       T3 
#> 32.76695 32.57543 32.66631 37.05902 37.15404 37.53580