Renyi entropy of order alpha — Renent • rmorie

$$H_\alpha(p) = \frac{1}{1-\alpha}\log\sum_k p_k^\alpha$$ with the removable cases taken as limits: $\alpha \to 1$ gives Shannon entropy, $\alpha \to \infty$ the min-entropy $-\log\max_k p_k$, and $\alpha = 0$ the log support size. $H_\alpha$ is non-increasing in alpha.

Usage

Renent(y, alpha = 2, base = 2)

Arguments

y: Counts or probabilities.
alpha: Order, non-negative; Inf gives the min-entropy.
base: Log base; 2 gives bits, NULL gives nats.

Value

Named list with estimate, alpha, base, probabilities, support, method.

References

Renyi (1961) Proc. 4th Berkeley Symp. 1:547-561.

Examples

Renent(c(0.5, 0.25, 0.25), 2)
#> $estimate
#> [1] 1.415037
#> 
#> $alpha
#> [1] 2
#> 
#> $base
#> [1] 2
#> 
#> $probabilities
#> [1] 0.50 0.25 0.25
#> 
#> $support
#> [1] 3
#> 
#> $method
#> [1] "Renyi entropy of order alpha (Renyi 1961)"
#>