# 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. 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.