Computes the general Shannon evenness index (aka Pielou's J), defined as the ratio of the observed Shannon entropy to the maximum possible entropy given the number of categories. This function is included here because Shannon evenness can be applied to stage-at-death distributions to quantify how evenly deaths are distributed across stages.
evenness_shannon(p)A numeric value between 0 and 1 representing Shannon evenness. A value of 1 indicates an even distribution, while low values indicate uneven distributions. A value of 0 indicates that all deaths are lumped into one stage.
Zero entries in p contribute nothing to entropy
but do count towards the total number of categories when computing
the maximum entropy (\(H_\max = \log(K)\)).
#Even
evenness_shannon(c(0.2,0.2,0.2,0.2,0.2))
#> [1] 1
#Skewed
evenness_shannon(c(0.8,0.1,0.05,0.03,0.02))
#> [1] 0.4610288
evenness_shannon(c(1,0,0,0,0))
#> [1] 0
#From a matrix model's stage at death distribution
data(mpm1)
matA <- mpm1$matU + mpm1$matF
ssd <- popdemo::eigs(matA, "ss")
x <- stage_at_death_dist(mpm1$matU, start = ssd)
evenness_shannon(x)
#> [1] 0.353197