boltzman_factor: Boltzmann's Factors

In genomaths/MethylIT: Methylation Analysis Based on Signal Detection

Boltzmann's Factors

Description

This function computes the Boltzmann's factors as function of addimensional Gibb entropy S/k_B (see gibb_entropy) and the expected value \nu of the generalized gamma (GG) distribution (with location parameter \mu = 0):

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

(see (Wikipedia))

The expected value \nu is given as:

\nu = \theta * \Gamma(\psi + 1/\alpha)/\Gamma(\psi)

(\\theta = scale)

Usage

boltzman_factor(model = NULL, pars, ...)

## S4 method for signature 'missingORNULL'
boltzman_factor(model, pars, only.sum = TRUE)

## S4 method for signature 'cdfMODEL'
boltzman_factor(model, only.sum = TRUE)

## S4 method for signature 'cdfMODELlist'
boltzman_factor(model, only.sum = TRUE)

## S4 method for signature 'ProbDistrList'
boltzman_factor(model, only.sum = TRUE)

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.
pars	Optional. A numerical vector containing the model parameter values in the given in order: alpha, scale, and delta.
only.sum	If only.sum = TRUE, then only the sum of Boltzmann's factors is returned.

Details

The Boltzmann's factor of Gibb entropy S/k_B is given as:

exp(-abs(S)/k_B)

While the Boltzmann's factor of \nu is calculated as:

exp(-\eqn{\nu})

Value

Boltzmann's factors exp(-abs(S)/k_B), exp(-\nu), and exp(-abs(S)/k_B) + exp(-\nu), and the expected values \nu and the variance \sigma = \theta^2 Gamma(\psi + 2/\alpha)/\Gamma(\psi). If only.sum = TRUE (default), the only the sum of Boltzmann's factors is returned.

See Also

gibb_entropy

Examples

## Loading the probability distribution models
data(gof, "MethylIT")
## Gibb entropy in J * (K * mol)^-1)
gibb_entropy(gof)
## Shannon entropy
gibb_entropy(gof, R = 1, log.base = 2)

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