summ_entropy() computes entropy of single distribution while summ_entropy2() - for a pair of distributions. For "discrete" pdqr-functions a classic formula -sum(p * log(p)) (in nats) is used. In "continuous" case a differential entropy is computed.

summ_entropy(f)

summ_entropy2(f, g, method = "relative", clip = exp(-20))

## Arguments

f A pdqr-function representing distribution. A pdqr-function. Should be the same type as f. Entropy method for pair of distributions. One of "relative" (Kullback–Leibler divergence) or "cross" (for cross-entropy). Value to be used instead of 0 during log() computation. -log(clip) represents the maximum value of output entropy.

## Value

A single number representing entropy. If clip is strictly positive, then it will be finite.

## Details

Note that due to pdqr approximation error there can be a rather big error in entropy estimation in case original density goes to infinity.

Other summary functions: summ_center(), summ_classmetric(), summ_distance(), summ_hdr(), summ_interval(), summ_moment(), summ_order(), summ_prob_true(), summ_pval(), summ_quantile(), summ_roc(), summ_separation(), summ_spread()

## Examples

d_norm <- as_d(dnorm)
d_norm_2 <- as_d(dnorm, mean = 2, sd = 0.5)

summ_entropy(d_norm)#> [1] 1.418913summ_entropy2(d_norm, d_norm_2)#> [1] 9.006174summ_entropy2(d_norm, d_norm_2, method = "cross")#> [1] 10.42509
# Increasing clip leads to decreasing maximum output value
d_1 <- new_d(1:10, "discrete")
d_2 <- new_d(20:21, "discrete")

# Formally, output isn't clearly defined because functions don't have the
# same support. Direct use of entropy formulas gives infinity output, but
# here maximum value is -log(clip).
summ_entropy2(d_1, d_2, method = "cross")#> [1] 20summ_entropy2(d_1, d_2, method = "cross", clip = exp(-10))#> [1] 10summ_entropy2(d_1, d_2, method = "cross", clip = 0)#> [1] Inf