God's unbiased estimator

The mean rarity perspective suggests a novel approach to estimating true diversity from a sample, using the fact that the sample mean is an unbiased estimate of the population mean. Although how to estimate a species’ rarity from sample data remains unsolved, we test the promise of this idea using what we call God’s estimator: All-knowing, God can plug in the true population parameters for each species. Nevertheless, maybe for fun, God chooses to compute the sample mean, weighting species’ true rarities by their sampled frequency.

GUE(freqs, true_p, l, q = NULL)

Arguments

freqs

Non-negative numeric vector of observed species frequencies

true_p

Non-negative numeric vector of true, population-level species frequencies

l

Scaling exponent for the mean, can be any real number.

q

Scalar, traditional Hill number scaling exponent, q = 1-l where l is the scaling parameter for the generalized mean. Can be any real number.

Examples

GUE(freqs =  1:10/sum(1:10), true_p =  1:10/sum(1:10), l = 1) # true richness 10
#> [1] 10
GUE(freqs =  rep(1:5,2)/sum(1:10), true_p =  1:10/sum(1:10), l = 1) # true richness 10
#> [1] 12.41501