KLq {entropart} | R Documentation |

## 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 |

### 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

### 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)
```

*entropart*version 1.6-13 Index]