Generalized Kullback-Leibler divergence

Calculates the generalized Kullback-Leibler divergence between an observed and an expected probability distribution.

Usage

KLq(Ps, Pexp, q = 1, CheckArguments = TRUE)

Arguments

Ps

The observed probability vector.

Pexp

The expected probability vector.

q

A number: the order of entropy. Default is 1.

CheckArguments

Logical; if TRUE, the function arguments are verified. Should be set to FALSE to save time when the arguments have been checked elsewhere.

Details

The generalized Kullback-Leibler divergence (Borland et al., 1998) converges to the Kullback-Leibler divergence (Kullback and Leibler, 1951) when \(q\) tends to 1. It is used to calculate the generalized beta entropy (Marcon et al., 2014).

Value

A number equal to the generalized Kullback-Leibler divergence between the probability distributions.

References

Borland, L., Plastino, A. R. and Tsallis, C. (1998). Information gain within nonextensive thermostatistics. Journal of Mathematical Physics 39(12): 6490-6501.

Kullback, S. and Leibler, R. A. (1951). On Information and Sufficiency. The Annals of Mathematical Statistics 22(1): 79-86.

Marcon, E., Scotti, I., Herault, B., Rossi, V. and Lang, G. (2014). Generalization of the partitioning of Shannon diversity. PLOS One 9(3): e90289.

See also

TsallisBeta

Examples

# Load Paracou data (number of trees per species in two 1-ha plot of a tropical forest)
data(Paracou618)
# Ps is the vector of probabilities
Ps <- Paracou618.MC$Ps
# Probability distribution of the first plot
Ps1 <- Paracou618.MC$Psi[, 1]
# Divergence of order 2 between the first plot and the whole forest
KLq(Ps1, Ps, 2)
#> [1] 0.01004705