skbio.diversity.alpha.esty_ci

skbio.diversity.alpha.esty_ci(counts)[source]

Calculate Esty’s CI.

State: Experimental as of 0.4.0.

Esty’s CI is defined as

\[F_1/N \pm z\sqrt{W}\]

where \(F_1\) is the number of singleton OTUs, \(N\) is the total number of individuals (sum of abundances for all OTUs), and \(z\) is a constant that depends on the targeted confidence and based on the normal distribution.

\(W\) is defined as

\[\frac{F_1(N-F_1)+2NF_2}{N^3}\]

where \(F_2\) is the number of doubleton OTUs.

Parameters

counts (1-D array_like, int) – Vector of counts.

Returns

Esty’s confidence interval as (lower_bound, upper_bound).

Return type

tuple

Notes

Esty’s CI is defined in 1. \(z\) is hardcoded for a 95% confidence interval.

References

1

Esty, W. W. (1983). “A normal limit law for a nonparametric estimator of the coverage of a random sample”. Ann Statist 11: 905-912.