def get_poisson_distribution(date_range, country_code, global_min, global_max):
"""
Args:
date_range (pandas.core.series.Series): The date range of country data for the poisson distribution to be applied to.
country_code (string): The country code of the country being explored.
global_min (pandas.core.series.Series): A time series list of the global minimum tendencies for tor users.
global_max (pandas.core.series.Series): A time series list of the global maximum tendencies for tor users.
"""
current_date = date_range[0]
comparison_date = date_range[1]
#print(date_range)
# If there is not a global min or a global max on the day in question then don't even try
if pd.isnull(global_min[date_range.name]) or pd.isnull(global_max[date_range.name]):
return pd.Series({"country":country_code,"min":None, "max":None})
# We can't do this without both dates
if np.isnan(comparison_date) or np.isnan(current_date):
return pd.Series({"country":country_code,"min":None, "max":None})
else:
down_score = 0
up_score = 0
# poisson.ppf(plausable_range, shape_params)
min_range = global_min[date_range.name] * poisson.ppf(1-0.9999, comparison_date)
max_range = global_max[date_range.name] * poisson.ppf(0.9999, comparison_date)
if current_date < min_range:
down_score = 1
if current_date > max_range:
up_score = 1
return pd.Series({"country":country_code,"min":min_range, "max":max_range, "users":current_date, "event_censor":down_score, "event_spike":up_score})
def CorrectInitialCorrel(lambda1, lambda2, r):
samples = 500
u = np.random.uniform(low=0, high=1, size=samples)
maxcor = pearsonr(poisson.ppf(u, lambda1), poisson.ppf(u, lambda2))
mincor = pearsonr(poisson.ppf(u, lambda1), poisson.ppf(1 - u, lambda2))
a = -maxcor[0] * mincor[0] / (maxcor[0] + mincor[0])
b = np.log((maxcor[0] + a) / a)
c = -a
corrected = np.log((r + a) / a) / b
return np.NaN if corrected > 1 or corrected < -1 else corrected
def absolute_plot(series, minc, maxc, labels,INTERVAL, xtitle):
in_minc = []
in_maxc = []
for i, v in enumerate(series):
if i > 0 and i - INTERVAL >= 0 and series[i] != None and series[i-INTERVAL] != None and series[i-INTERVAL] != 0 and minc[i]!= None and maxc[i]!= None:
in_minc += [minc[i] * poisson.ppf(1-0.9999, series[i-INTERVAL])]
in_maxc += [maxc[i] * poisson.ppf(0.9999, series[i-INTERVAL])]
if not in_minc[-1] < in_maxc[-1]:
print in_minc[-1], in_maxc[-1], series[i-INTERVAL], minc[i], maxc[i]
assert in_minc[-1] < in_maxc[-1]
else:
in_minc += [None]
in_maxc += [None]
raw_plot(series, in_minc, in_maxc, labels, xtitle)
def write_all(tss, minc, maxc, INTERVAL=7):
ranges_file = file("direct-users-ranges.csv", "w")
ranges_file.write("date,country,minusers,maxusers\n")
exclude = set(["all", "??", "date"])
for c in tss.country_codes:
if c in exclude:
continue
series = tss.get_country_series(c)
for i, v in enumerate(series):
if i > 0 and i - INTERVAL >= 0 and series[i] != None and series[i-INTERVAL] != None and series[i-INTERVAL] != 0 and minc[i]!= None and maxc[i]!= None:
minv = minc[i] * poisson.ppf(1-0.9999, series[i-INTERVAL])
maxv = maxc[i] * poisson.ppf(0.9999, series[i-INTERVAL])
if not minv < maxv:
print minv, maxv, series[i-INTERVAL], minc[i], maxc[i]
assert minv < maxv
ranges_file.write("%s,%s,%s,%s\n" % (tss.all_dates[i], c, minv, maxv))
ranges_file.close()
def censor_score(series, minc, maxc, INTERVAL, scoring_interval=None):
upscore = 0
downscore = 0
if scoring_interval is None:
scoring_interval = len(series)
assert(len(series) >= scoring_interval)
for i, v in enumerate(series):
if i > 0 and i - INTERVAL >= 0 and series[i] != None and series[i-INTERVAL] != None and series[i-INTERVAL] != 0 and minc[i]!= None and maxc[i]!= None:
in_minc = minc[i] * poisson.ppf(1-0.9999, series[i-INTERVAL])
in_maxc = maxc[i] * poisson.ppf(0.9999, series[i-INTERVAL])
if (i >= (len(series) - scoring_interval)):
downscore += 1 if minc[i] != None and v < in_minc else 0
upscore += 1 if maxc[i] != None and v > in_maxc else 0
return downscore, upscore
def GenerateMultivariatePoisson(p, samples, R, lmbda):
normal_mu = np.repeat(0, p) # Dimensions of Distribution
normal = np.random.multivariate_normal(mean=normal_mu, cov=R,
size=samples).T
p = norm.cdf(normal)
pois = poisson.ppf(p, lmbda) # Inverse Poisson Distribution
return pois
def censor_score(series, minc, maxc, INTERVAL, scoring_interval=None):
upscore = 0
downscore = 0
if scoring_interval is None:
scoring_interval = len(series)
assert (len(series) >= scoring_interval)
for i, v in enumerate(series):
if i > 0 and i - INTERVAL >= 0 and series[i] != None and series[
i - INTERVAL] != None and series[
i - INTERVAL] != 0 and minc[i] != None and maxc[i] != None:
in_minc = minc[i] * poisson.ppf(1 - 0.9999, series[i - INTERVAL])
in_maxc = maxc[i] * poisson.ppf(0.9999, series[i - INTERVAL])
if (i >= (len(series) - scoring_interval)):
downscore += 1 if minc[i] != None and v < in_minc else 0
upscore += 1 if maxc[i] != None and v > in_maxc else 0
return downscore, upscore
def absolute_plot(series, minc, maxc, labels, INTERVAL, xtitle):
in_minc = []
in_maxc = []
for i, v in enumerate(series):
if i > 0 and i - INTERVAL >= 0 and series[i] != None and series[
i - INTERVAL] != None and series[
i - INTERVAL] != 0 and minc[i] != None and maxc[i] != None:
in_minc += [
minc[i] * poisson.ppf(1 - 0.9999, series[i - INTERVAL])
]
in_maxc += [maxc[i] * poisson.ppf(0.9999, series[i - INTERVAL])]
if not in_minc[-1] < in_maxc[-1]:
print in_minc[-1], in_maxc[-1], series[
i - INTERVAL], minc[i], maxc[i]
assert in_minc[-1] < in_maxc[-1]
else:
in_minc += [None]
in_maxc += [None]
raw_plot(series, in_minc, in_maxc, labels, xtitle)
def write_all(tss, minc, maxc, RANGES_FILE, INTERVAL=7):
ranges_file = file(RANGES_FILE, "w")
ranges_file.write("date,country,minusers,maxusers\n")
exclude = set(["all", "??", "date"])
for c in tss.country_codes:
if c in exclude:
continue
series = tss.get_country_series(c)
for i, v in enumerate(series):
if i > 0 and i - INTERVAL >= 0 and series[i] != None and series[
i - INTERVAL] != None and series[
i -
INTERVAL] != 0 and minc[i] != None and maxc[i] != None:
minv = minc[i] * poisson.ppf(1 - 0.9999, series[i - INTERVAL])
maxv = maxc[i] * poisson.ppf(0.9999, series[i - INTERVAL])
if not minv < maxv:
print minv, maxv, series[i - INTERVAL], minc[i], maxc[i]
assert minv < maxv
ranges_file.write("%s,%s,%s,%s\n" %
(tss.all_dates[i], c, minv, maxv))
ranges_file.close()
z[:, j] = a * z[:, j - 1] + np.sqrt(1 - a**2) * z[:, j]
u = norm.cdf(z)
# The covariates
x1 = np.random.normal(size=(n, q))
x2 = np.random.normal(size=(n, q))
# The mean parameters for the marginal distributions
lpr = x1 - 0.5 * x2
expval = np.exp(lpr)
# The response values. These are marginally Poisson with the specified means.
y = np.zeros((n, q))
for i in range(n):
for j in range(q):
y[i, j] = poisson.ppf(u[i, j], expval[i, j])
idv = np.outer(np.arange(n), np.ones(q))
time = np.outer(np.ones(n), np.arange(q))
df = pd.DataFrame({
"y": y.flat,
"x1": x1.flat,
"x2": x2.flat,
"grp": idv.flat,
"time": time.flat
})
model = sm.GEE.from_formula("y ~ x1 + x2",
groups="grp",
family=sm.families.Poisson(),
def negbinom(u, mu, scale):
p = (scale - 1) / scale
r = mu * (1 - p) / p
x = np.random.gamma(r, p / (1 - p), len(u))
return poisson.ppf(u, mu=x)