def __init__(self, lower, upper):
if lower is None:
self.lower = 0.0
else:
self.lower = lower
if upper is None:
self.upper = 1.0
else:
self.upper = upper
if self.lower > self.upper:
raise ValueError(
'Invalid Beta distribution parameters. Lower should be smaller than upper.'
)
self.bounds = np.array([self.lower, self.upper])
self.x_range_for_pdf = np.linspace(self.lower, self.upper,
RECURRENCE_PDF_SAMPLES)
loc = self.lower
scale = self.upper - self.lower
self.parent = arcsine(loc=loc, scale=scale)
self.mean, self.variance, self.skewness, self.kurtosis = self.parent.stats(
moments='mvsk')
self.shape_parameter_A = -0.5
self.shape_parameter_B = -0.5
mean, var, skew, kurt = arcsine.stats(moments='mvsk')
# Display the probability density function (``pdf``):
x = np.linspace(arcsine.ppf(0.01),
arcsine.ppf(0.99), 100)
ax.plot(x, arcsine.pdf(x),
'r-', lw=5, alpha=0.6, label='arcsine 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 = arcsine()
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = arcsine.ppf([0.001, 0.5, 0.999])
np.allclose([0.001, 0.5, 0.999], arcsine.cdf(vals))
# True
# Generate random numbers:
r = arcsine.rvs(size=1000)
# And compare the histogram:
ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
def all_dists():
# dists param were taken from scipy.stats official
# documentaion examples
# Total - 89
return {
"alpha":
stats.alpha(a=3.57, loc=0.0, scale=1.0),
"anglit":
stats.anglit(loc=0.0, scale=1.0),
"arcsine":
stats.arcsine(loc=0.0, scale=1.0),
"beta":
stats.beta(a=2.31, b=0.627, loc=0.0, scale=1.0),
"betaprime":
stats.betaprime(a=5, b=6, loc=0.0, scale=1.0),
"bradford":
stats.bradford(c=0.299, loc=0.0, scale=1.0),
"burr":
stats.burr(c=10.5, d=4.3, loc=0.0, scale=1.0),
"cauchy":
stats.cauchy(loc=0.0, scale=1.0),
"chi":
stats.chi(df=78, loc=0.0, scale=1.0),
"chi2":
stats.chi2(df=55, loc=0.0, scale=1.0),
"cosine":
stats.cosine(loc=0.0, scale=1.0),
"dgamma":
stats.dgamma(a=1.1, loc=0.0, scale=1.0),
"dweibull":
stats.dweibull(c=2.07, loc=0.0, scale=1.0),
"erlang":
stats.erlang(a=2, loc=0.0, scale=1.0),
"expon":
stats.expon(loc=0.0, scale=1.0),
"exponnorm":
stats.exponnorm(K=1.5, loc=0.0, scale=1.0),
"exponweib":
stats.exponweib(a=2.89, c=1.95, loc=0.0, scale=1.0),
"exponpow":
stats.exponpow(b=2.7, loc=0.0, scale=1.0),
"f":
stats.f(dfn=29, dfd=18, loc=0.0, scale=1.0),
"fatiguelife":
stats.fatiguelife(c=29, loc=0.0, scale=1.0),
"fisk":
stats.fisk(c=3.09, loc=0.0, scale=1.0),
"foldcauchy":
stats.foldcauchy(c=4.72, loc=0.0, scale=1.0),
"foldnorm":
stats.foldnorm(c=1.95, loc=0.0, scale=1.0),
# "frechet_r": stats.frechet_r(c=1.89, loc=0.0, scale=1.0),
# "frechet_l": stats.frechet_l(c=3.63, loc=0.0, scale=1.0),
"genlogistic":
stats.genlogistic(c=0.412, loc=0.0, scale=1.0),
"genpareto":
stats.genpareto(c=0.1, loc=0.0, scale=1.0),
"gennorm":
stats.gennorm(beta=1.3, loc=0.0, scale=1.0),
"genexpon":
stats.genexpon(a=9.13, b=16.2, c=3.28, loc=0.0, scale=1.0),
"genextreme":
stats.genextreme(c=-0.1, loc=0.0, scale=1.0),
"gausshyper":
stats.gausshyper(a=13.8, b=3.12, c=2.51, z=5.18, loc=0.0, scale=1.0),
"gamma":
stats.gamma(a=1.99, loc=0.0, scale=1.0),
"gengamma":
stats.gengamma(a=4.42, c=-3.12, loc=0.0, scale=1.0),
"genhalflogistic":
stats.genhalflogistic(c=0.773, loc=0.0, scale=1.0),
"gilbrat":
stats.gilbrat(loc=0.0, scale=1.0),
"gompertz":
stats.gompertz(c=0.947, loc=0.0, scale=1.0),
"gumbel_r":
stats.gumbel_r(loc=0.0, scale=1.0),
"gumbel_l":
stats.gumbel_l(loc=0.0, scale=1.0),
"halfcauchy":
stats.halfcauchy(loc=0.0, scale=1.0),
"halflogistic":
stats.halflogistic(loc=0.0, scale=1.0),
"halfnorm":
stats.halfnorm(loc=0.0, scale=1.0),
"halfgennorm":
stats.halfgennorm(beta=0.675, loc=0.0, scale=1.0),
"hypsecant":
stats.hypsecant(loc=0.0, scale=1.0),
"invgamma":
stats.invgamma(a=4.07, loc=0.0, scale=1.0),
"invgauss":
stats.invgauss(mu=0.145, loc=0.0, scale=1.0),
"invweibull":
stats.invweibull(c=10.6, loc=0.0, scale=1.0),
"johnsonsb":
stats.johnsonsb(a=4.32, b=3.18, loc=0.0, scale=1.0),
"johnsonsu":
stats.johnsonsu(a=2.55, b=2.25, loc=0.0, scale=1.0),
"ksone":
stats.ksone(n=1e03, loc=0.0, scale=1.0),
"kstwobign":
stats.kstwobign(loc=0.0, scale=1.0),
"laplace":
stats.laplace(loc=0.0, scale=1.0),
"levy":
stats.levy(loc=0.0, scale=1.0),
"levy_l":
stats.levy_l(loc=0.0, scale=1.0),
"levy_stable":
stats.levy_stable(alpha=0.357, beta=-0.675, loc=0.0, scale=1.0),
"logistic":
stats.logistic(loc=0.0, scale=1.0),
"loggamma":
stats.loggamma(c=0.414, loc=0.0, scale=1.0),
"loglaplace":
stats.loglaplace(c=3.25, loc=0.0, scale=1.0),
"lognorm":
stats.lognorm(s=0.954, loc=0.0, scale=1.0),
"lomax":
stats.lomax(c=1.88, loc=0.0, scale=1.0),
"maxwell":
stats.maxwell(loc=0.0, scale=1.0),
"mielke":
stats.mielke(k=10.4, s=3.6, loc=0.0, scale=1.0),
"nakagami":
stats.nakagami(nu=4.97, loc=0.0, scale=1.0),
"ncx2":
stats.ncx2(df=21, nc=1.06, loc=0.0, scale=1.0),
"ncf":
stats.ncf(dfn=27, dfd=27, nc=0.416, loc=0.0, scale=1.0),
"nct":
stats.nct(df=14, nc=0.24, loc=0.0, scale=1.0),
"norm":
stats.norm(loc=0.0, scale=1.0),
"pareto":
stats.pareto(b=2.62, loc=0.0, scale=1.0),
"pearson3":
stats.pearson3(skew=0.1, loc=0.0, scale=1.0),
"powerlaw":
stats.powerlaw(a=1.66, loc=0.0, scale=1.0),
"powerlognorm":
stats.powerlognorm(c=2.14, s=0.446, loc=0.0, scale=1.0),
"powernorm":
stats.powernorm(c=4.45, loc=0.0, scale=1.0),
"rdist":
stats.rdist(c=0.9, loc=0.0, scale=1.0),
"reciprocal":
stats.reciprocal(a=0.00623, b=1.01, loc=0.0, scale=1.0),
"rayleigh":
stats.rayleigh(loc=0.0, scale=1.0),
"rice":
stats.rice(b=0.775, loc=0.0, scale=1.0),
"recipinvgauss":
stats.recipinvgauss(mu=0.63, loc=0.0, scale=1.0),
"semicircular":
stats.semicircular(loc=0.0, scale=1.0),
"t":
stats.t(df=2.74, loc=0.0, scale=1.0),
"triang":
stats.triang(c=0.158, loc=0.0, scale=1.0),
"truncexpon":
stats.truncexpon(b=4.69, loc=0.0, scale=1.0),
"truncnorm":
stats.truncnorm(a=0.1, b=2, loc=0.0, scale=1.0),
"tukeylambda":
stats.tukeylambda(lam=3.13, loc=0.0, scale=1.0),
"uniform":
stats.uniform(loc=0.0, scale=1.0),
"vonmises":
stats.vonmises(kappa=3.99, loc=0.0, scale=1.0),
"vonmises_line":
stats.vonmises_line(kappa=3.99, loc=0.0, scale=1.0),
"wald":
stats.wald(loc=0.0, scale=1.0),
"weibull_min":
stats.weibull_min(c=1.79, loc=0.0, scale=1.0),
"weibull_max":
stats.weibull_max(c=2.87, loc=0.0, scale=1.0),
"wrapcauchy":
stats.wrapcauchy(c=0.0311, loc=0.0, scale=1.0),
}
axis.set_xlim([0.0, 3.0])
axis.set_ylim([0.0, 2.0])
axis.yaxis.set_ticks([0.0, 0.5, 1.0, 1.5, 2.0])
axis.set_title(f"Weibull Distribution: λ=1.0")
for i in range(len(k)):
pdf = stats.weibull(k[i], 1.0)
pdf_values = [pdf(j) for j in x]
axis.plot(x, pdf_values, label=f"k={k[i]}")
axis.legend()
config.save_post_asset(figure, "metropolis_hastings_sampling", "weibull_distribution_parameters")
# %%
## arcsine
x = numpy.linspace(0.001, 0.999, 200)
pdf = [stats.arcsine(j) for j in x]
figure, axis = pyplot.subplots(figsize=(10, 7))
axis.set_xlabel("X")
axis.set_ylabel("PDF")
axis.set_xlim([0.0, 1.0])
axis.set_title(f"Arcsine Distribution")
axis.plot(x, pdf)
config.save_post_asset(figure, "metropolis_hastings_sampling", "arcsine_distribution_parameters")
# %%
## bimodal normal
x = numpy.linspace(-7.0, 7.0, 200)
pdf = [stats.bimodal_normal(j, 1.2) for j in x]
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import scipy.stats as sts
# %matplotlib inline
# Сгенерируем выборку объёма 1000 из arcsine распределения
arcsine_rv = sts.arcsine()
sample = arcsine_rv.rvs(1000)
# Гистограмма выборки и теоретическая плотность распределения поверх нее:
plt.hist(sample, normed=True)
plt.ylabel('number of samples')
# на том же графике построим теоретическую плотность распределения:
x = np.linspace(0, 1, 1000)
pdf = arcsine_rv.pdf(x)
plt.plot(x, pdf, label='theoretical pdf', alpha=0.5)
plt.legend()
plt.ylabel('$f(x)$')
plt.xlabel('$x$')
def histogram(n, mean, variance):
# Генерируем 1000 выборочных средних
mead_sample = [np.mean(arcsine_rv.rvs(n)) for i in range(1000)]
# Строим нормальное распределение на основе значений дисперсии и мат. ожидания
norm_rv = sts.norm(mean, np.sqrt(variance / n))
# Строим гистограмму распределения выборочных средних
def arcsine(n=100, loc=0, scale=1):
'''
arcsine distribution
n - розмір вибірки
loc - середина
scale - відхилення
Повертає список вигляду [згенерована вибірка, список x, список y, середнє, мода, медіана,
розмах, девіація, варіанса, стандарт, варіація, асиметрія, ексцес]
'''
distribution = st.arcsine(loc=loc, scale=scale)
sample = list(distribution.rvs(size=n))
for i in range(len(sample)):
sample[i] = round(sample[i], 2)
var = list(sample)
var.sort()
x = list(set(sample))
y = list()
x.sort()
freq_table = dict()
for num in x:
freq_table[num] = sample.count(num)
int_len = ((max(sample) - min(sample)) / r(sample))
int_bounds = list()
next = min(sample)
for i in range(r(sample)):
int_bounds.append(round(next, 2))
next += int_len
int_bounds.append(max(sample))
freq_table = dict()
int_list = list()
for i in range(len(int_bounds) - 1):
int_list.append([int_bounds[i], int_bounds[i + 1]])
for i in range(len(int_list)):
if i != len(int_list) - 1:
freq_table["[" + str(int_list[i][0]) + "; " + str(int_list[i][1]) +
")"] = 0
else:
freq_table["[" + str(int_list[i][0]) + "; " + str(int_list[i][1]) +
"]"] = 0
for i in range(len(sample)):
for j in range(len(int_list)):
if sample[i] >= int_list[j][0] and sample[i] < int_list[j][
1] and j != len(int_list) - 1:
freq_table["[" + str(int_list[j][0]) + "; " +
str(int_list[j][1]) + ")"] += 1
elif sample[i] >= int_list[j][0] and sample[i] <= int_list[j][
1] and j == len(int_list) - 1:
freq_table["[" + str(int_list[j][0]) + "; " +
str(int_list[j][1]) + "]"] += 1
int_list_values = list()
for key in freq_table:
int_list_values.append(int(freq_table[key]))
intr = list(freq_table.keys())
centered_int = list()
for intr in int_list:
centered_int.append(round(((intr[0] + intr[1]) / 2), 3))
freq_table_disc = dict()
x = list(set(sample))
for num in x:
freq_table_disc[num] = sample.count(num)
result = list()
result.append(sample)
start = distribution.ppf(0.01)
end = distribution.ppf(0.99)
x = list(np.linspace(start, end, n))
y = list(distribution.pdf(x))
result.append(x)
result.append(y)
mean = np.mean(sample)
result.append(mean)
moda = list(mode(freq_table_disc).keys())
result.append(moda)
med = statistics.median(sample)
result.append(med)
ro = max(sample) - min(sample)
result.append(ro)
deviation = dev(freq_table_disc)
result.append(deviation)
variansa = dev(freq_table_disc) / (len(sample) - 1)
result.append(variansa)
standart = math.sqrt(variansa)
result.append(standart)
variation = standart / np.mean(sample)
asym = st.skew(sample)
result.append(asym)
ex = st.kurtosis(sample)
result.append(ex)
return result