skbio.diversity.alpha.esty_ci

skbio.diversity.alpha.esty_ci(counts)

Calculate Esty’s confidence interval of Good’s coverage estimator.

Esty’s confidence interval is defined as

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

where \(F_1\) is the number of singleton taxa, \(N\) is the total number of individuals, 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 taxa.

Parameters:

counts1-D array_like, int

Vector of counts.

Returns:

tuple

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

Notes

Esty’s confidence interval was originally described 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.