def proposal(x): """ This is symmetric proposal PDF to plot the sample path """ # return cauchy.rvs(loc=x, scale=0.15, size=1) # return norm.rvs(loc=x, scale=0.2, size=1) return logistic.rvs(loc=x, scale=1, size=1)
def generateSamples(self):
if self.sourceType == 'white':
self.data = np.append(self.data, np.random.normal(size=self.sampleGain))
elif self.sourceType == 'const':
self.data = np.append(self.data, np.zeros(self.sampleGain))
elif self.sourceType == 'logistic':
self.data = np.append(self.data, logistic.rvs(size=self.sampleGain))
self.transformedData = self.transformation(self.data)
def logistic_distribution(par_size, par_scale):
logis = logistic.rvs(size=par_size, scale=par_scale)
x_logistic = []
logistic_data = []
for i in range(0, len(logis)):
x_logistic.append(i)
logistic_data.append([i, logis[i]])
print(logistic_data)
plt.plot(x_logistic, logis)
plt.show()
return logistic_data
def gen_sample(self, n):
return logistic.rvs(loc=self.mu, scale=self.sigma, size=n)
res = minimize(training_loss,
jac=training_loss_jac,
x0=fit_params,
method="BFGS",
options={
"maxiter": maxiter,
"gtol": tol
})
print(res)
final_params = res.x
for i in range(num):
final_params[2 * i + 1] = np.exp(final_params[2 * i + 1])
results = []
for i in range(num):
results.append(final_params[2 * i])
results.append(
logistic.isf(
0.25, loc=final_params[2 * i], scale=final_params[2 * i + 1]) -
final_params[2 * i])
for i in range(num - 1):
results.append(final_params[2 * num + i])
return results
data = logistic.rvs(loc=10, scale=5, size=200)
print(estimate(data, 2))
print("True likelihood:", log_likelihood_logistic(data, [10, np.log(5)]))
def bootstrap(a,
f=None,
b=100,
method="balanced",
family=None,
strata=None,
smooth=False,
random_state=None):
"""
Calculate function values from bootstrap samples or
optionally return bootstrap samples themselves
Parameters
----------
a : array-like
Original sample
f : callable or None
Function to be bootstrapped
b : int
Number of bootstrap samples
method : string
* 'ordinary'
* 'balanced'
* 'parametric'
family : string or None
* 'gaussian'
* 't'
* 'laplace'
* 'logistic'
* 'F'
* 'gamma'
* 'log-normal'
* 'inverse-gaussian'
* 'pareto'
* 'beta'
* 'poisson'
strata : array-like or None
Stratification labels, ignored when method
is parametric
smooth : boolean
Whether or not to add noise to bootstrap
samples, ignored when method is parametric
random_state : int or None
Random number seed
Returns
-------
y | X : np.array
Function applied to each bootstrap sample
or bootstrap samples if f is None
"""
np.random.seed(random_state)
a = np.asarray(a)
n = len(a)
# stratification not meaningful for parametric sampling
if strata is not None and (method != "parametric"):
strata = np.asarray(strata)
if len(strata) != len(a):
raise ValueError("a and strata must have" " the same length")
# recursively call bootstrap without stratification
# on the different strata
masks = [strata == x for x in np.unique(strata)]
boot_strata = [
bootstrap(a=a[m],
f=None,
b=b,
method=method,
strata=None,
random_state=random_state) for m in masks
]
# concatenate resampled strata along first column axis
X = np.concatenate(boot_strata, axis=1)
else:
if method == "ordinary":
# i.i.d. sampling from ecdf of a
X = np.reshape(a[np.random.choice(range(a.shape[0]),
a.shape[0] * b)],
newshape=(b, ) + a.shape)
elif method == "balanced":
# permute b concatenated copies of a
r = np.reshape([a] * b, newshape=(b * a.shape[0], ) + a.shape[1:])
X = np.reshape(r[np.random.permutation(range(r.shape[0]))],
newshape=(b, ) + a.shape)
elif method == "parametric":
if len(a.shape) > 1:
raise ValueError("a must be one-dimensional")
# fit parameters by maximum likelihood and sample
if family == "gaussian":
theta = norm.fit(a)
arr = norm.rvs(size=n * b,
loc=theta[0],
scale=theta[1],
random_state=random_state)
elif family == "t":
theta = t.fit(a, fscale=1)
arr = t.rvs(size=n * b,
df=theta[0],
loc=theta[1],
scale=theta[2],
random_state=random_state)
elif family == "laplace":
theta = laplace.fit(a)
arr = laplace.rvs(size=n * b,
loc=theta[0],
scale=theta[1],
random_state=random_state)
elif family == "logistic":
theta = logistic.fit(a)
arr = logistic.rvs(size=n * b,
loc=theta[0],
scale=theta[1],
random_state=random_state)
elif family == "F":
theta = F.fit(a, floc=0, fscale=1)
arr = F.rvs(size=n * b,
dfn=theta[0],
dfd=theta[1],
loc=theta[2],
scale=theta[3],
random_state=random_state)
elif family == "gamma":
theta = gamma.fit(a, floc=0)
arr = gamma.rvs(size=n * b,
a=theta[0],
loc=theta[1],
scale=theta[2],
random_state=random_state)
elif family == "log-normal":
theta = lognorm.fit(a, floc=0)
arr = lognorm.rvs(size=n * b,
s=theta[0],
loc=theta[1],
scale=theta[2],
random_state=random_state)
elif family == "inverse-gaussian":
theta = invgauss.fit(a, floc=0)
arr = invgauss.rvs(size=n * b,
mu=theta[0],
loc=theta[1],
scale=theta[2],
random_state=random_state)
elif family == "pareto":
theta = pareto.fit(a, floc=0)
arr = pareto.rvs(size=n * b,
b=theta[0],
loc=theta[1],
scale=theta[2],
random_state=random_state)
elif family == "beta":
theta = beta.fit(a)
arr = beta.rvs(size=n * b,
a=theta[0],
b=theta[1],
loc=theta[2],
scale=theta[3],
random_state=random_state)
elif family == "poisson":
theta = np.mean(a)
arr = poisson.rvs(size=n * b,
mu=theta,
random_state=random_state)
else:
raise ValueError("Invalid family")
X = np.reshape(arr, newshape=(b, n))
else:
raise ValueError("method must be either 'ordinary'"
" , 'balanced', or 'parametric',"
" '{method}' was supplied".format(method=method))
# samples are already smooth in the parametric case
if smooth and (method != "parametric"):
X += np.random.normal(size=X.shape, scale=1 / np.sqrt(n))
if f is None:
return X
else:
return np.asarray([f(x) for x in X])
# Display the probability density function (``pdf``): x = np.linspace(logistic.ppf(0.01), logistic.ppf(0.99), 100) ax.plot(x, logistic.pdf(x), 'r-', lw=5, alpha=0.6, label='logistic 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 = logistic() ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') # Check accuracy of ``cdf`` and ``ppf``: vals = logistic.ppf([0.001, 0.5, 0.999]) np.allclose([0.001, 0.5, 0.999], logistic.cdf(vals)) # True # Generate random numbers: r = logistic.rvs(size=1000) # And compare the histogram: ax.hist(r, density=True, histtype='stepfilled', alpha=0.2) ax.legend(loc='best', frameon=False) plt.show()
