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:
$$\nu = \theta * \Gamma(\psi + 1/\alpha)/\Gamma(\psi)$$
(\(\\theta = scale\))
boltzman_factor(model = NULL, pars, ...)
# S4 method for missingORNULL
boltzman_factor(model, pars, only.sum = TRUE)
# S4 method for cdfMODEL
boltzman_factor(model, only.sum = TRUE)
# S4 method for cdfMODELlist
boltzman_factor(model, only.sum = TRUE)
# S4 method for ProbDistrList
boltzman_factor(model, only.sum = TRUE)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.
Optional. A numerical vector containing the model parameter values in the given in order: alpha, scale, and delta.
If only.sum = TRUE, then only the sum of Boltzmann's factors is returned.
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.
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:
$$exp(-\eqn{\nu})$$
## 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
## Shannon entropy
gibb_entropy(gof, R = 1, log.base = 2)
#> C1 C2 C3 T1 T2 T3
#> 5.262539 5.220933 5.235455 5.698251 5.567555 5.824454