skbio.math.diversity.alpha.esty_ci

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

Calculate Esty’s CI.

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:

tuple

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

Notes

Esty’s CI is defined in [R38]. \(z\) is hardcoded for a 95% confidence interval.

References

[R38](1, 2) Esty, W. W. (1983). “A normal limit law for a nonparametric estimator of the coverage of a random sample”. Ann Statist 11: 905-912.