def esty_ci(counts, **args):
"""Esty's CI for (1-m).
counts: Vector of counts (NOT the sample)
Esty's CI is defined in
Esty WW (1983) A Normal limit law for a nonparametric estimator of the
coverage of a random sample. Ann Statist 11: 905-912.
n1 / n +/- z * square-root(W);
where
n1 = number of species observed once in n samples;
n = sample size;
z = a constant that depends on the targeted confidence and based on
the Normal distribution. For a 95% CI, z=1.959963985;
n2 = number of species observed twice in n samples;
W = [ n1*(n - n1) + 2*n*n2 ] / (n**3).
Note: for other confidence levels we first need the appropriate z,
Not yet hooked up to CLI.
Returns: (upper bound, lower bound)
"""
n1 = singles(counts)
n2 = doubles(counts)
n = counts.sum()
z = 1.959963985
W = (n1*(n-n1) + 2*n*n2)/(n**3)
return n1/n + z*sqrt(W), n1/n - z*sqrt(W)
def test_singles(self):
"""singles should return correct # of singles"""
self.assertEqual(singles(self.TestData), 3)
self.assertEqual(singles(array([0,3,4])), 0)
self.assertEqual(singles(array([1])), 1)