test_anderson_darling.py

import numpy as np
import scipy.stats

from test_kuiper import seed, double_check, check_uniform, check_fpp, check_fpp_kuiper
import anderson_darling

def F(x):
    return anderson_darling.anderson_darling(x)[-1]


def test_fpp_values():
    for (f, p)  in [(1.9329578, 0.9),
                   (2.492367, 0.95), 
                   (3.878125, 0.99),
                   (9, 0.999960466)]:
        assert np.abs(anderson_darling.anderson_darling_fpp(f)-(1-p))<0.0001

def test_uniform():
    for N in 20, 100, 1000:
        yield check_uniform, F, N

@seed()
@double_check
def test_non_null():
    A2, fpp = anderson_darling.anderson_darling(np.random.random(1000)/2)
    assert fpp<0.01


def test_fpp():
    for N in 10, 50, 100:
        yield check_fpp, F, N, 1000, 0.05
        yield check_fpp_kuiper, F, N, 1000


@seed()
@double_check
def check_fpp_ad_nonuniform(N, M, cdf, cdfinv):
    r = []
    for i in range(M):
        s = cdfinv(np.random.random(N))
        A2, fpp = anderson_darling.anderson_darling(s,cdf)
        r.append(fpp)
    assert anderson_darling.anderson_darling(r)>0.01

def test_fpp_nonuniform():
    for N in 10, 50, 100:
        yield check_fpp_ad_nonuniform, N, 1000, np.exp, np.log
        yield check_fpp_ad_nonuniform, N, 1000, lambda x: x**3, lambda x: x**(1./3)

        yield check_fpp_kuiper, F, N, 1000

@seed()
@double_check
def check_k_sample_fpp(ip, p, k, m):
    N = 1000
    r = 0
    for i in range(N):
        samples = np.random.random_sample((k,m))
        A2, TkN, (tkm1, ps), pv = anderson_darling.anderson_darling_k(samples)
        if pv<=p:
            r += 1
    assert scipy.stats.binom(N,p).cdf(r) > 0.01
    assert scipy.stats.binom(N,p).sf(r) > 0.01

def test_k_sample_fpp():

    for ip, p in enumerate([0.25, 0.10, 0.05, 0.025, 0.01]):
        yield check_k_sample_fpp, ip, p, 2, 10
        yield check_k_sample_fpp, ip, p, 10, 10

@seed()
@double_check
def test_k_sample_simple_pass():
    samples = np.random.random_sample((2,10))
    A2, TkN, (tkm1, ps), pv = anderson_darling.anderson_darling_k(samples)
    assert pv>0.01 # 0.01 is the smallest possible p

@seed()
@double_check
def test_k_sample_simple_fail():
    samples = np.random.random_sample((2,100))
    samples[1,:] *= 2
    A2, TkN, (tkm1, ps), pv = anderson_darling.anderson_darling_k(samples)
    assert pv<=0.01 # 0.01 is the smallest possible p

@seed()
@double_check
def check_normal_fpp(n, mu, sigma, p):
    if mu is None:
        m = 0
    else:
        m = mu
    if sigma is None:
        s = 1
    else:
        s = sigma

    N = 1000
    r = 0
    for i in range(N):
        d = np.random.standard_normal(n) * s + m
        A2, (mu_, sigma_), (ps, ths), pi = anderson_darling.anderson_darling_normal(d, mu=mu, sigma=sigma)
        if pi<=p:
            r+=1
    assert scipy.stats.binom(N,p).cdf(r) > 0.01
    assert scipy.stats.binom(N,p).sf(r) > 0.01

def test_normal_fpp():
    for n in [10, 100, 1000]:
        yield check_normal_fpp, n, 0, 1, 0.1
        yield check_normal_fpp, n, None, 1, 0.1
        yield check_normal_fpp, n, 0, None, 0.1
        yield check_normal_fpp, n, None, None, 0.1
        yield check_normal_fpp, n, 0, 1, 0.01
        yield check_normal_fpp, n, None, 1, 0.01
        yield check_normal_fpp, n, 0, None, 0.01
        yield check_normal_fpp, n, None, None, 0.01