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
\[\frac{F_1(NF_1)+2NF_2}{N^3}\]where \(F_2\) is the number of doubleton OTUs.
 Parameters
counts (1D array_like, int) – Vector of counts.
 Returns
Esty’s confidence interval as
(lower_bound, upper_bound)
. Return type
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: 905912.