def z_bi_cephes(n_on, n_off, alpha):
tau = 1.0 / alpha
aa = n_on
bb = n_off + 1
xx = 1.0 / (1 + tau)
# Checks to avoid Nan in some cases
if aa <= 0.0 or bb <= 0.0:
return 0.0
if xx <= 0.0:
return 0.0
if xx >= 1.0:
return 1.0
# I use the incbet from cephes instead of the scipy.special.betainc function because the latter has numerical
# problems in some instances and return Nans, while the incbet from Cephes is more robust
P_Bi = incbet(aa, bb, xx)
return significance_from_pvalue(P_Bi)
def frequency_test(obs1, tot1, obs2, tot2):
"""
:param obs1: (int) the count number of an amino acid X in the set of protein 1.
:param tot1: (int) the total number of amino acids in the set of protein 1.
:param obs2: (int) the count number of an amino acid X in the set of protein 2.
:param tot2: (int) the total number of amino acids in the set of protein 2.
:return: proportion test p-value
"""
mean1 = float(obs1) / tot1
mean2 = float(obs2) / tot2
var1 = float(obs1) * (1 - mean1) * (1 - mean1) + (tot1 - obs1) * mean1 * mean1
var2 = float(obs2) * (1 - mean2) * (1 - mean2) + (tot2 - obs2) * mean2 * mean2
df = tot1 + tot2 - 2
svar = (var1 + var2) / df
t = (mean1-mean2) / sqrt(svar*(1.0/tot1 + 1.0/tot2))
return cprob.incbet(0.5*df, 0.5, df/(df+t*t))
def _incbet(a, b, x):
return incbet(a, b, x)
def test_incbet():
assert_almost_equal(cprob.incbet(1., 3., 0.3), 0.657)