Hill numbers of order q

qD = (sum_i p_i^q)^(1/(1-q)) for q != 1, and 1D = exp(-sum_i p_i log p_i) in the limit q -> 1.

Usage

Hillq(x, q = 1)

Arguments

x

Non-negative abundances or proportions; closed internally.

q

Order of the diversity number.

Value

List with hill, q, prop, richness, shannon, simpson, D.

References

Hill, M. O. (1973), Ecology 54(2), 427-432, Equation (2) and Sect. 2. Standard published form; standard published form.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Hillq(V)
#> $hill
#> [1] 6.936504
#> 
#> $q
#> [1] 1
#> 
#> $prop
#> [1] 0.02777778 0.05555556 0.08333333 0.11111111 0.13888889 0.16666667 0.19444444
#> [8] 0.22222222
#> 
#> $richness
#> [1] 8
#> 
#> $shannon
#> [1] 1.936798
#> 
#> $simpson
#> [1] 0.1574074
#> 
#> $D
#> [1] 8
#> 
#> $method
#> [1] "Hill number of order q (Hill 1973 eq. 2)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"