def test_weightstats_2(self):
x1, x2 = self.x1, self.x2
w1, w2 = self.w1, self.w2
d1 = DescrStatsW(x1)
d1w = DescrStatsW(x1, weights=w1)
d2w = DescrStatsW(x2, weights=w2)
x1r = d1w.asrepeats()
x2r = d2w.asrepeats()
# print 'random weights'
# print ttest_ind(x1, x2, weights=(w1, w2))
# print stats.ttest_ind(x1r, x2r)
assert_almost_equal(ttest_ind(x1, x2, weights=(w1, w2))[:2],
stats.ttest_ind(x1r, x2r), 14)
# not the same as new version with random weights/replication
# assert x1r.shape[0] == d1w.sum_weights
# assert x2r.shape[0] == d2w.sum_weights
assert_almost_equal(x2r.mean(0), d2w.mean, 14)
assert_almost_equal(x2r.var(), d2w.var, 14)
assert_almost_equal(x2r.std(), d2w.std, 14)
# note: the following is for 1d
assert_almost_equal(np.cov(x2r, bias=1), d2w.cov, 14)
# assert_almost_equal(np.corrcoef(np.x2r), d2w.corrcoef, 19)
# TODO: exception in corrcoef (scalar case)
# one-sample tests
# print d1.ttest_mean(3)
# print stats.ttest_1samp(x1, 3)
# print d1w.ttest_mean(3)
# print stats.ttest_1samp(x1r, 3)
assert_almost_equal(d1.ttest_mean(3)[:2], stats.ttest_1samp(x1, 3), 11)
assert_almost_equal(d1w.ttest_mean(3)[:2],
stats.ttest_1samp(x1r, 3), 11)
def test_weightstats_2(self):
x1, x2 = self.x1, self.x2
w1, w2 = self.w1, self.w2
d1 = DescrStatsW(x1)
d1w = DescrStatsW(x1, weights=w1)
d2w = DescrStatsW(x2, weights=w2)
x1r = d1w.asrepeats()
x2r = d2w.asrepeats()
# print 'random weights'
# print ttest_ind(x1, x2, weights=(w1, w2))
# print stats.ttest_ind(x1r, x2r)
assert_almost_equal(
ttest_ind(x1, x2, weights=(w1, w2))[:2], stats.ttest_ind(x1r, x2r),
14)
#not the same as new version with random weights/replication
# assert x1r.shape[0] == d1w.sum_weights
# assert x2r.shape[0] == d2w.sum_weights
assert_almost_equal(x2r.mean(0), d2w.mean, 14)
assert_almost_equal(x2r.var(), d2w.var, 14)
assert_almost_equal(x2r.std(), d2w.std, 14)
#note: the following is for 1d
assert_almost_equal(np.cov(x2r, bias=1), d2w.cov, 14)
#assert_almost_equal(np.corrcoef(np.x2r), d2w.corrcoef, 19)
#TODO: exception in corrcoef (scalar case)
#one-sample tests
# print d1.ttest_mean(3)
# print stats.ttest_1samp(x1, 3)
# print d1w.ttest_mean(3)
# print stats.ttest_1samp(x1r, 3)
assert_almost_equal(d1.ttest_mean(3)[:2], stats.ttest_1samp(x1, 3), 11)
assert_almost_equal(
d1w.ttest_mean(3)[:2], stats.ttest_1samp(x1r, 3), 11)
def compute_summary_statistics(dbm: database_manager.DatabaseManager, tbl_name: str) -> Optional[Dict[str, Tuple]]:
"""
Computes summary statistics for given table.
:param dbm: A DatabaseManager instance.
:param tbl_name: name of the table to compute monthly return for.
:return: dictionary containing various statistics.
"""
df, info, start_date = finance_metrics.compute_monthly_returns(dbm, tbl_name)
if df is not None and info is not None:
stat = {}
dsw = DescrStatsW(df['Monthly_Return'].values)
stat['table_name'] = tbl_name
stat['contract_name'] = info[1]
stat['type'] = info[3] if info[3] is not None else None
stat['subtype'] = info[4] if info[4] is not None else None
stat['start-date'] = start_date
stat['ar'] = df['Monthly_Return'].mean() * 12
stat['vol'] = df['Monthly_Return'].std() * np.sqrt(12)
stat['t-stat'] = dsw.ttest_mean(alternative='larger')[0]
stat['p-value'] = dsw.ttest_mean(alternative='larger')[1]
stat['kurt'] = df['Monthly_Return'].kurt()
stat['skew'] = df['Monthly_Return'].skew()
return stat
return None
def test_weightstats_2(self):
x1, x2 = self.x1, self.x2
w1, w2 = self.w1, self.w2
d1 = DescrStatsW(x1)
d1w = DescrStatsW(x1, weights=w1)
d2w = DescrStatsW(x2, weights=w2)
x1r = d1w.asrepeats()
x2r = d2w.asrepeats()
# print 'random weights'
# print ttest_ind(x1, x2, weights=(w1, w2))
# print stats.ttest_ind(x1r, x2r)
assert_almost_equal(ttest_ind(x1, x2, weights=(w1, w2))[:2],
stats.ttest_ind(x1r, x2r), 14)
#not the same as new version with random weights/replication
# assert x1r.shape[0] == d1w.sum_weights
# assert x2r.shape[0] == d2w.sum_weights
assert_almost_equal(x2r.var(), d2w.var, 14)
assert_almost_equal(x2r.std(), d2w.std, 14)
#one-sample tests
# print d1.ttest_mean(3)
# print stats.ttest_1samp(x1, 3)
# print d1w.ttest_mean(3)
# print stats.ttest_1samp(x1r, 3)
assert_almost_equal(d1.ttest_mean(3)[:2], stats.ttest_1samp(x1, 3), 11)
assert_almost_equal(d1w.ttest_mean(3)[:2], stats.ttest_1samp(x1r, 3), 11)
def test_weightstats_3(self):
x1_2d, x2_2d = self.x1_2d, self.x2_2d
w1, w2 = self.w1, self.w2
d1w_2d = DescrStatsW(x1_2d, weights=w1)
d2w_2d = DescrStatsW(x2_2d, weights=w2)
x1r_2d = d1w_2d.asrepeats()
x2r_2d = d2w_2d.asrepeats()
assert_almost_equal(x2r_2d.mean(0), d2w_2d.mean, 14)
assert_almost_equal(x2r_2d.var(0), d2w_2d.var, 14)
assert_almost_equal(x2r_2d.std(0), d2w_2d.std, 14)
assert_almost_equal(np.cov(x2r_2d.T, bias=1), d2w_2d.cov, 14)
assert_almost_equal(np.corrcoef(x2r_2d.T), d2w_2d.corrcoef, 14)
# print d1w_2d.ttest_mean(3)
# #scipy.stats.ttest is also vectorized
# print stats.ttest_1samp(x1r_2d, 3)
t, p, d = d1w_2d.ttest_mean(3)
assert_almost_equal([t, p], stats.ttest_1samp(x1r_2d, 3), 11)
#print [stats.ttest_1samp(xi, 3) for xi in x1r_2d.T]
cm = CompareMeans(d1w_2d, d2w_2d)
ressm = cm.ttest_ind()
resss = stats.ttest_ind(x1r_2d, x2r_2d)
assert_almost_equal(ressm[:2], resss, 14)
def test_weightstats_3(self):
x1_2d, x2_2d = self.x1_2d, self.x2_2d
w1, w2 = self.w1, self.w2
d1w_2d = DescrStatsW(x1_2d, weights=w1)
d2w_2d = DescrStatsW(x2_2d, weights=w2)
x1r_2d = d1w_2d.asrepeats()
x2r_2d = d2w_2d.asrepeats()
assert_almost_equal(x2r_2d.mean(0), d2w_2d.mean, 14)
assert_almost_equal(x2r_2d.var(0), d2w_2d.var, 14)
assert_almost_equal(x2r_2d.std(0), d2w_2d.std, 14)
assert_almost_equal(np.cov(x2r_2d.T, bias=1), d2w_2d.cov, 14)
assert_almost_equal(np.corrcoef(x2r_2d.T), d2w_2d.corrcoef, 14)
# print d1w_2d.ttest_mean(3)
# #scipy.stats.ttest is also vectorized
# print stats.ttest_1samp(x1r_2d, 3)
t, p, d = d1w_2d.ttest_mean(3)
assert_almost_equal([t, p], stats.ttest_1samp(x1r_2d, 3), 11)
# print [stats.ttest_1samp(xi, 3) for xi in x1r_2d.T]
cm = CompareMeans(d1w_2d, d2w_2d)
ressm = cm.ttest_ind()
resss = stats.ttest_ind(x1r_2d, x2r_2d)
assert_almost_equal(ressm[:2], resss, 14)
def test_weightstats_ddof_tests(self):
# explicit test that ttest and confint are independent of ddof
# one sample case
x1_2d = self.x1_2d
w1 = self.w1
d1w_d0 = DescrStatsW(x1_2d, weights=w1, ddof=0)
d1w_d1 = DescrStatsW(x1_2d, weights=w1, ddof=1)
d1w_d2 = DescrStatsW(x1_2d, weights=w1, ddof=2)
#check confint independent of user ddof
res0 = d1w_d0.ttest_mean()
res1 = d1w_d1.ttest_mean()
res2 = d1w_d2.ttest_mean()
# concatenate into one array with np.r_
assert_almost_equal(np.r_[res1], np.r_[res0], 14)
assert_almost_equal(np.r_[res2], np.r_[res0], 14)
res0 = d1w_d0.ttest_mean(0.5)
res1 = d1w_d1.ttest_mean(0.5)
res2 = d1w_d2.ttest_mean(0.5)
assert_almost_equal(np.r_[res1], np.r_[res0], 14)
assert_almost_equal(np.r_[res2], np.r_[res0], 14)
#check confint independent of user ddof
res0 = d1w_d0.tconfint_mean()
res1 = d1w_d1.tconfint_mean()
res2 = d1w_d2.tconfint_mean()
assert_almost_equal(res1, res0, 14)
assert_almost_equal(res2, res0, 14)
def test_weightstats_ddof_tests(self):
# explicit test that ttest and confint are independent of ddof
# one sample case
x1_2d = self.x1_2d
w1 = self.w1
d1w_d0 = DescrStatsW(x1_2d, weights=w1, ddof=0)
d1w_d1 = DescrStatsW(x1_2d, weights=w1, ddof=1)
d1w_d2 = DescrStatsW(x1_2d, weights=w1, ddof=2)
# check confint independent of user ddof
res0 = d1w_d0.ttest_mean()
res1 = d1w_d1.ttest_mean()
res2 = d1w_d2.ttest_mean()
# concatenate into one array with np.r_
assert_almost_equal(np.r_[res1], np.r_[res0], 14)
assert_almost_equal(np.r_[res2], np.r_[res0], 14)
res0 = d1w_d0.ttest_mean(0.5)
res1 = d1w_d1.ttest_mean(0.5)
res2 = d1w_d2.ttest_mean(0.5)
assert_almost_equal(np.r_[res1], np.r_[res0], 14)
assert_almost_equal(np.r_[res2], np.r_[res0], 14)
# check confint independent of user ddof
res0 = d1w_d0.tconfint_mean()
res1 = d1w_d1.tconfint_mean()
res2 = d1w_d2.tconfint_mean()
assert_almost_equal(res1, res0, 14)
assert_almost_equal(res2, res0, 14)
def one_t_test(pdf, data_measlevs, var_name, test_value=0):
"""One sample t-test
arguments:
var_name (str):
Name of the variable to test.
test_value (numeric):
Test against this value.
return:
text_result (html str):
Result in APA format.
image (matplotlib):
Bar chart with mean and confidence interval.
"""
text_result = ''
data = pdf[var_name].dropna()
if data_measlevs[var_name] in ['int', 'unk']:
if data_measlevs[var_name] == 'unk':
text_result += warn_unknown_variable
if len(set(data)) == 1:
return _('One sample t-test cannot be run for constant variable.\n'
), None
data = pdf[var_name].dropna()
descr = DescrStatsW(data)
t, p, df = descr.ttest_mean(float(test_value))
if LooseVersion(csc.versions['statsmodels']) >= LooseVersion('0.5'):
# Or we could use confidence_interval_t
cil, cih = descr.tconfint_mean()
ci = (cih - cil) / 2
prec = cs_util.precision(data) + 1
ci_text = '[%0.*f, %0.*f]' % (prec, cil, prec, cih)
else:
ci = 0 # only with statsmodels
ci_text = _(
'Sorry, newer statsmodels module is required for confidence interval.\n'
)
text_result += _('One sample t-test against %g') % float(
test_value) + ': <i>t</i>(%d) = %0.3g, %s\n' % (df, t,
cs_util.print_p(p))
# Graph
image = cs_chart.create_variable_population_chart(data, var_name, ci)
else:
text_result += _(
'One sample t-test is computed only for interval variables.')
image = None
return ci_text, text_result, image
def test_weightstats_3(self):
x1_2d, x2_2d = self.x1_2d, self.x2_2d
w1, w2 = self.w1, self.w2
d1w_2d = DescrStatsW(x1_2d, weights=w1)
d2w_2d = DescrStatsW(x2_2d, weights=w2)
x1r_2d = d1w_2d.asrepeats()
x2r_2d = d2w_2d.asrepeats()
# print d1w_2d.ttest_mean(3)
# #scipy.stats.ttest is also vectorized
# print stats.ttest_1samp(x1r_2d, 3)
t,p,d = d1w_2d.ttest_mean(3)
assert_almost_equal([t, p], stats.ttest_1samp(x1r_2d, 3), 11)
#print [stats.ttest_1samp(xi, 3) for xi in x1r_2d.T]
ressm = CompareMeans(d1w_2d, d2w_2d).ttest_ind()
resss = stats.ttest_ind(x1r_2d, x2r_2d)
assert_almost_equal(ressm[:2], resss, 14)
def compute_rule(self):
daily_ret_log = np.log(self.daily_ret + 1)
df = pd.DataFrame()
N = self.daily_ret.shape[0]
iter = 0
for asset in daily_ret_log.columns:
print('TREND Progress: {}%'.format(
int(iter * 100 / daily_ret_log.shape[1])))
data = daily_ret_log[asset]
first_not_null = 0
t_scores = []
for i in range(N):
if np.isnan(data.iloc[i]):
first_not_null += 1
# TODO verify
t_scores.append(0)
continue
if i <= first_not_null + self.lookback:
t_scores.append(0)
continue
stats = DescrStatsW(data.iloc[i - self.lookback:i])
if stats.std_mean == 0:
print('Period of all zeroes for asset {} from {}'.format(
asset, data.index[i - self.lookback]))
t_scores.append(0)
continue
t_scores.append(stats.ttest_mean(0, 'larger')[0])
df[asset] = np.clip(t_scores, -1.0, 1.0)
iter += 1
df['index'] = self.daily_ret.index
df.set_index('index', inplace=True)
return df
my_knn_socres = cross_val_score(KNeighborsRegressor(n_neighbors=5),
X,
y,
cv=LeaveOneOut(),
scoring='neg_mean_squared_error')
(-my_lm_scores.mean())**0.5
#> 15.697306009399101 # 線形回帰分析
(-my_knn_socres.mean())**0.5
#> 16.07308308943869 # K最近傍法
my_df = pd.DataFrame({'lm': -my_lm_scores, 'knn': -my_knn_socres})
my_df.head()
#> lm knn
#> 0 18.913720 108.16
#> 1 179.215044 0.64
#> 2 41.034336 64.00
#> 3 168.490212 184.96
#> 4 5.085308 0.00
my_df.boxplot().set_ylabel("$r^2$")
from statsmodels.stats.weightstats import DescrStatsW
d = DescrStatsW(my_df.lm - my_df.knn)
d.ttest_mean()[1] # p値
#> 0.6952755720536115
d.tconfint_mean(alpha=0.05, alternative='two-sided') # 信頼区間
#> (-72.8275283312228, 48.95036023665703)
X = [
32.1, 26.2, 27.5, 31.8, 32.1, 31.2, 30.1, 32.4, 32.3, 29.9, 29.6, 26.6,
31.2, 30.9, 29.3
]
Y = [
35.4, 34.6, 31.1, 32.4, 33.3, 34.7, 35.3, 34.3, 32.1, 28.3, 33.3, 30.5,
32.6, 33.3, 32.2
]
a = 0.05 # 有意水準（デフォルト） = 1 - 信頼係数
alt = 'two-sided' # 両側検定（デフォルト）
# 左片側検定なら'smaller'
# 右片側検定なら'larger'
d = DescrStatsW(np.array(X) - np.array(Y)) # 対標本の場合
d.ttest_mean(alternative=alt)[1] # p値
#> 0.0006415571512322235
d.tconfint_mean(alpha=a, alternative=alt) # 信頼区間
#> (-3.9955246743198867, -1.3644753256801117)
c = CompareMeans(DescrStatsW(X), DescrStatsW(Y)) # 対標本でない場合
ve = 'pooled' # 等分散を仮定する（デフォルト）．仮定しないなら'unequal'．
c.ttest_ind(alternative=alt, usevar=ve)[1] # p値
#> 0.000978530937238609
c.tconfint_diff(alpha=a, alternative=alt, usevar=ve) # 信頼区間
#> (-4.170905570517185, -1.1890944294828283)
### 4.4.4 独立性の検定（カイ2乗検定）
# Critério do valor p
# Teste Unicaudal Superior
# Rejeitar H_0 se o valor p\leq\alpha
p_valor = t_student.sf(t, df=24)
p_valor <= significancia
# Outra forma de obter a resposta
from statsmodels.stats.weightstats import DescrStatsW
test = DescrStatsW(amostra)
t, p_valor, df = test.ttest_mean(value=media, alternative='larger')
print('Valor de t', t[0])
print('P-valor', p_valor[0])
print('Média do data frame ', df)
p_valor[0] <= significancia
# Conclusão: Com um nível de confiança de 95% não podemos rejeitar H_0,
# ou seja, a alegação do fabricante é verdadeira
# Teste Duas Variáveis
# Seleção das amostras
df.head()
df['Species'].unique()
