Tsallis entropy of the empirical distribution of a sample

Shannon entropy is additive. Tsallis replaces the logarithm with a power, and independent systems then pick up a (1 - q) S_A S_B cross term – the point of the generalisation rather than a defect. As q -> 1 the expression tends to Shannon, and that limit is returned exactly at q = 1 rather than dividing by zero.

Usage

Tsallen(y, q)

Arguments

y

Sample; the empirical pmf over distinct values is used.

q

Entropic index; q = 1 gives Shannon entropy in nats.

Value

List with estimate, n_categories, n, q.

Details

Formula: S_q = (1 / (q - 1)) (1 - sum_x p(x)^q).

References

Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. J Stat Phys 52:479-487, equation (1).

Examples

Tsallen(y = c(1, 2, 3, 4, 5, 6, 7, 8), q = 0.5)
#> $estimate
#> [1] 3.656854
#> 
#> $n_categories
#> [1] 8
#> 
#> $n
#> [1] 8
#> 
#> $q
#> [1] 0.5
#> 
#> $method
#> [1] "Tsallis q-entropy of the empirical pmf"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"