entropart (version 1.4-8)

KLq: Generalized Kullback-Leibler divergence

Description

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.

Value

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

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).

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

# NOT RUN {
  # 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)
# }