This function computes the contribution of a molecular machine (methylation molecular machinery) to the entropy of individual methylation system, which is estimated for members of the Generalized Gamma (GG) Distribution family. GG density is given as:
\(exp(-y^\alpha) * \alpha*y^{\alpha*\psi - 1}/(scale*\gamma(\psi))\)
(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)).
machine_ent(model, R = 8.31446261815324, ...)
# S4 method for missing_OR_NULL
machine_ent(model, R = 8.31446261815324, pars, only.mchent = FALSE)
# S4 method for cdfMODEL
machine_ent(model, R = 8.31446261815324, only.mchent = FALSE)
# S4 method for cdfMODELlist
machine_ent(model, R = 8.31446261815324, only.mchent = FALSE)
# S4 method for ProbDistrList
machine_ent(model, R = 8.31446261815324, only.mchent = FALSE)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.
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.
Optional. A numerical vector containing the model parameter values in the given in order: alpha, scale, and delta.
Molecular machine contribution to the methylation entropy based on the model provided.
The entropy contribution derives from the GG model as given by
functions nonlinearFitDist and gofReport. Given
the model parameters \(\alpha\) and \(\psi\) the molecular machine
contribution to the methylation system's entropy is given by the equation:
$$digamma(\psi) * ((1/\alpha) - \psi) + \psi$$
where digamma is the first derivative of the logarithm of
the gamma function
(Wikipedia).
The value of the constant R can be simply 1, which returns the Shannon entropy in bit units, only carrying informational meaning.
Crooks, Gavin E. (2015) The Amoroso Distribution. arXiv:1005.3274v2.