def binomial_exact(successes, trials, prob):
"""Returns binomial probability of exactly X successes.
Works for integer and floating point values.
Note: this function is only a probability mass function for integer
values of 'trials' and 'successes', i.e. if you sum up non-integer
values you probably won't get a sum of 1.
"""
if (prob < 0) or (prob > 1):
raise ValueError("Binomial prob must be between 0 and 1.")
if (successes < 0) or (trials < successes):
raise ValueError("Binomial successes must be between 0 and trials.")
return exp(ln_binomial(successes, trials, prob))
def test_ln_binomial_range(self):
"""ln_binomial should increase in a monotonically increasing region."""
start = 0
end = 1
step = 0.1
lower_lim = -1.783375 - 1e-4
upper_lim = -1.021235 + 1e-4
previous_value = -1.784
while start <= end:
obs = ln_binomial(start, 5, 0.3)
assert lower_lim <= obs <= upper_lim
assert obs > previous_value
previous_value = obs
start += step
def test_ln_binomial_floats(self):
"""Binomial exact should match values from R for integer successes"""
expected = {
(18.3, 100, 0.2): (math.log(0.09089812), math.log(0.09807429)),
(2.7, 1050, 0.006): (math.log(0.03615498), math.log(0.07623827)),
(2.7, 1050, 0.06): (math.log(1.365299e-25), math.log(3.044327e-24)),
(2, 100.5, 0.6): (math.log(7.303533e-37), math.log(1.789727e-36)),
(0.2, 60, 0.5): (math.log(8.673617e-19), math.log(5.20417e-17)),
(0.5, 5, 0.3): (math.log(0.16807), math.log(0.36015)),
(10, 100.5, 0.5): (math.log(7.578011e-18), math.log(1.365543e-17)),
}
for (key, value) in list(expected.items()):
min_val, max_val = value
assert min_val < ln_binomial(*key) < max_val
def test_ln_binomial_integer(self):
"""ln_binomial should match R results for integer values"""
expected = {
(10, 60, 0.1): -3.247883,
(1, 1, 0.5): math.log(0.5),
(1, 1, 0.0000001): math.log(1e-07),
(1, 1, 0.9999999): math.log(0.9999999),
(3, 5, 0.75): math.log(0.2636719),
(0, 60, 0.5): math.log(8.673617e-19),
(129, 130, 0.5): math.log(9.550892e-38),
(299, 300, 0.099): math.log(1.338965e-298),
(9, 27, 0.0003): math.log(9.175389e-26),
(1032, 2050, 0.5): math.log(0.01679804),
}
for (key, value) in list(expected.items()):
self.assertFloatEqualRel(ln_binomial(*key), value, 1e-4)
