def _posterior(df, r, c, col='new', a=1, b=3, gamma=GAMMA):
df = df.copy()
posteriors(df, r, c, col, a, b)
df['data'] = df[col]
# Posterior on lambda, the daily rate of infection.
df['posterior'] = r*betaprime.median(df.alpha, df.beta)
df['pos5'] = r*betaprime.ppf(0.05, df.alpha, df.beta)
df['pos95'] = r*betaprime.ppf(0.95, df.alpha, df.beta)
df['r'] = (np.log(df.posterior.shift(-1)) - np.log(df.posterior))/GAMMA + 1
df['r5'] = (np.log(df.pos5.shift(-1)) - np.log(df.posterior))/GAMMA + 1
df['r95'] = (np.log(df.pos95.shift(-1)) - np.log(df.posterior))/GAMMA + 1
return df[~df.r.isna()]
def generate_betaprime(param_list):
"""
This method generates a list of pairs (quantile skewness, quantile kurtosis)
for inverse beta distribution with given parameters
:param param_list: dict[str, list[float]]
A dictionary with keys which correspond to the names of parameters of a
given distribution ('a' and 'b' in case of inverse beta distribution) and
values that store specific parameter ranges
:return: list[tuple[float, float]]
A list of pairs (quantile skewness, quantile kurtosis) which can be viewed
as a point and act as a representation of inverse beta distribution with
specific parameters on a Pearson System
"""
if len(param_list) == 0:
raise EmptyParametersDict(
'No parameter dictionary was provided for inverse beta distribution.'
)
if 'a' not in param_list or 'b' not in param_list:
raise WrongParameterName(
'Wrong parameter names provided for beta distribution.')
a_arr = param_list['a']
b_arr = param_list['b']
if len(a_arr) == 0:
raise EmptyParameterList(
'No parameter list was provided for parameter alpha of inverse beta distribution.'
)
if len(b_arr) == 0:
raise EmptyParameterList(
'No parameter list was provided for parameter beta of inverse beta distribution.'
)
st_arr = []
for curr_a in a_arr:
for curr_b in b_arr:
curr_e = [betaprime.ppf(o, curr_a, curr_b) for o in OCTILES]
curr_s = (curr_e[5] - 2 * curr_e[3] + curr_e[1]) / (curr_e[5] -
curr_e[1])
curr_t = (curr_e[6] - curr_e[4] + curr_e[2] -
curr_e[0]) / (curr_e[5] - curr_e[1])
st_arr.append((curr_s, curr_t))
return st_arr
from scipy.stats import betaprime
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
# Calculate a few first moments:
a, b = 5, 6
mean, var, skew, kurt = betaprime.stats(a, b, moments='mvsk')
# Display the probability density function (``pdf``):
x = np.linspace(betaprime.ppf(0.01, a, b),
betaprime.ppf(0.99, a, b), 100)
ax.plot(x, betaprime.pdf(x, a, b),
'r-', lw=5, alpha=0.6, label='betaprime pdf')
# Alternatively, the distribution object can be called (as a function)
# to fix the shape, location and scale parameters. This returns a "frozen"
# RV object holding the given parameters fixed.
# Freeze the distribution and display the frozen ``pdf``:
rv = betaprime(a, b)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = betaprime.ppf([0.001, 0.5, 0.999], a, b)
np.allclose([0.001, 0.5, 0.999], betaprime.cdf(vals, a, b))
# True
def f_measure_ppf(q, a, b):
from scipy.stats import betaprime
betaprime_ppf = betaprime.ppf(1 - q, a, b)
f_ppf = 1.0 / (1 + 0.5 * betaprime_ppf)
return f_ppf
def ppf(self, q):
from scipy.stats import betaprime
beta_prime_ppf = betaprime.ppf(1 - q, self.a, self.b)
f_ppf = 1.0 / (1 + 0.5 * beta_prime_ppf)
return f_ppf