import numpy as np
import pandas as pd
import scipy.stats as ss
import matplotlib
from matplotlib import pyplot as plt
%matplotlib inline
SEED = 1337

plt.rcParams["axes.labelsize"] = 16.
plt.rcParams["xtick.labelsize"] = 14.
plt.rcParams["ytick.labelsize"] = 14.
plt.rcParams["legend.fontsize"] = 12.
plt.rcParams["figure.figsize"] = [15., 6.]


##############


n = 100
m = 1000
norm = [ss.norm.rvs(loc=2, scale=1.5, size=n, random_state=i) for i in range(m)]
stats = np.array([np.mean(v) for v in norm])

print(np.mean(stats), np.std(stats, ddof=1))

data = pd.DataFrame({'norm': stats})
data.hist(bins='rice')
plt.show()


##################

def generate_sample(n):
    N = np.random.normal(3,1, n)
    U = np.random.uniform(-3, 0, n)
    b = np.random.binomial(n=1, p= 0.5, size=n)
    return N*b + U * (1-b)


sample = generate_sample(1000)
data = pd.DataFrame({'my sample': sample})

stats = data.apply([np.mean, np.median, np.std])
stats.loc['Q1'] = data.apply(np.quantile, q=0.25)
stats.loc['Q3'] = data.apply(np.quantile, q=0.75)
stats.loc['V'] = data.apply(np.var, ddof=1)
stats.loc['skew'] = data.apply(ss.skew)
stats.loc['kurtosis'] = data.apply(ss.kurtosis)
stats
data.hist(bins='rice')
plt.show()

# генерируем 1000 выборок и считаем выборочные средние
m_samples = [generate_sample(n) for i in range(m)]
stats = np.array([np.mean(v) for v in m_samples])

print(np.mean(stats), np.std(stats, ddof=1))

data = pd.DataFrame({'means of my samples': stats})
data.hist(bins='rice')
plt.show()


##################