import pandas as pd import numpy as np import matplotlib.pyplot as plt import seaborn as sns import rdata from statsmodels.distributions.empirical_distribution import ECDF from scipy.optimize import minimize from scipy.stats import norm, t, chi2, expon, uniform np.set_printoptions(precision=3) np.random.seed(13232)

# nacteni souboru path = './ex0211.rda' parsed = rdata.parser.parse_file(path) converted = rdata.conversion.convert(parsed) data = converted['ex0211'] data

# rozdeeni do dvou skupin ctl = data[data['Group'] == 'control'].drop(columns='Group') bcl = data[data['Group'] == 'bacilli'].drop(columns='Group')

ctl_mean, ctl_var, ctl_median = ctl['Lifetime'].mean() , ctl['Lifetime'].var(), ctl['Lifetime'].median() bcl_mean, bcl_var, bcl_median = bcl['Lifetime'].mean() , bcl['Lifetime'].var(), bcl['Lifetime'].median() print(f'Control group:\nMean: {ctl_mean:.2f}\nVariance: {ctl_var:.2f}\nMedian: {ctl_median:.2f}') print('=============') print(f'Bacilli group:\nMean: {bcl_mean:.2f}\nVariance: {bcl_var:.2f}\nMedian: {bcl_median:.2f}')

def plot_distr(arr, name): plt.figure(figsize=(16, 8)) plt.subplot(121) plt.title(f'Hustota pravdepodobnosti skupina {name}') sns.distplot(arr, hist=True, kde=True, bins=15); plt.subplot(122) plt.title(f'Distribucni funkce skupina {name}') ecdf = ECDF(arr) plt.plot(ecdf.x, ecdf.y) plt.xlabel('Lifetime') plt.ylabel('Pravdepodobnost') plt.grid() plt.show()

# Skupina "BAcili" plot_distr(bcl.values.reshape(1, -1)[0], 'Bacilli')

plot_distr(ctl.values.reshape(1, -1)[0], 'Control')

def get_params(loc, scale, distr): if distr == 'exp': return 1 / scale elif distr == 'unif': a = loc b = loc + scale return a, b elif distr == 'norm': return loc, scale def fit_distributions(val, name): # exp distribution Exp(lambda) exp_loc, exp_scale = expon.fit(val, floc=0) lmbd = get_params(exp_loc, exp_scale, 'exp') print(f'MLE odhad {name} ~ Exp(lambda={lmbd:.4f})') # normal distribution N(m, s) norm_loc, norm_scale = norm.fit(val) print(f'MLE odhad {name} ~ N(mean={norm_loc:.4f}, std={norm_scale})') # uniform distribution unif_loc, unif_scale = uniform.fit(val) a, b = get_params(unif_loc, unif_scale, 'unif') print(f'MLE odhad {name} ~ Unif({a}, {b})') # get best distribution distrs = ['norm', 'exp', 'unif'] dic = { 'norm': { 'function': norm, 'loc': norm_loc, 'scale': norm_scale, }, 'exp': { 'function': expon, 'loc': exp_loc, 'scale': exp_scale, }, 'unif': { 'function': uniform, 'loc': unif_loc, 'scale': unif_scale, } } res = [] for d in distrs: densities = dic[d]['function'].pdf(val, loc=dic[d]['loc'], scale=dic[d]['scale']) res.append(np.prod(densities)) best_d = distrs[np.argmax(res)] print(f'Nejlepsi odhad - {best_d}{get_params(dic[best_d]["loc"], dic[best_d]["scale"], best_d)} rozdeleni') plt.figure(figsize=(12, 8)) x = np.linspace(min(val), max(val), 1000) plt.hist(val, bins=20, density=True) plt.plot(x, expon.pdf(x, loc=exp_loc, scale=exp_scale), label='Exponential distr', linewidth=3) plt.plot(x, norm.pdf(x, loc=norm_loc, scale=norm_scale), label='Normal distr', linewidth=3) plt.plot(x, uniform.pdf(x, loc=unif_loc, scale=unif_scale), label='Uniform distr', linewidth=3) plt.legend() plt.title(f'{name} group') plt.show()

fit_distributions(bcl.values.reshape(1, -1)[0], 'bacilli')

fit_distributions(ctl.values.reshape(1, -1)[0], 'control')

# bacilli samples = norm.rvs(loc=242.5345, scale=116.9098, size=100, random_state=42) plt.figure(figsize=(10, 6)) plt.hist(samples, alpha=0.7, label='generated', density=True) plt.hist(bcl.values, alpha=0.7, label='real', density=True) plt.legend() plt.show()

# control samples = uniform.rvs(loc=18, scale=717, size=100, random_state=42) plt.figure(figsize=(10, 6)) plt.hist(samples, alpha=0.7, label='generated', density=True) plt.hist(ctl.values, alpha=0.7, label='real', density=True) plt.legend()

# Method, implements sequence of actions to calculate 2 sided CI with distribution t def calculate_full_ci(data, target, group_name, alpha, logs=True): if target != None: X = data[target] else: X = data n = len(data) Xn = sum(X) / n s2 = sum((X - Xn) ** 2) / (n - 1) s = np.sqrt(s2) krit_hodnota = t.isf(alpha/2, df=n-1) delta = krit_hodnota * s / np.sqrt(n) IS = np.array([Xn - delta, Xn + delta]) if logs == True: print('\nSkupina {0}:'.format(group_name)) print('{0}% kritická hodnota rozdělení t:\nt({1})={2:.4f}' .format(100*alpha/2, alpha/2, krit_hodnota)) print('Oboustranný IS: ', IS) return IS

# Skupina "Control" IS_c = calculate_full_ci(ctl, 'Lifetime', 'Control', 0.05, logs=True) # Skupina "Bacilli" IS_b = calculate_full_ci(bcl, 'Lifetime', 'Bacilli', 0.05, logs=True)

def check_hypotesis(k, IS): res = k < IS[0] or k > IS[1] if res == True: print('Hypotezu odmitame.') else: print('Hypotezu neodmitame.')

alpha = 0.05 K = 20 print(f'Hypoteza: stredni hodnota = {K}') # Skupina "Control" print('\nSkupina "Control":') res_ctl = check_hypotesis(K ,IS_c) print('\nSkupina "Bacilli":') res_ctl = check_hypotesis(K ,IS_b)

# code X_ctl = ctl['Lifetime'].values X_bcl = bcl['Lifetime'].values X_ctl = np.random.choice(X_ctl, size=len(X_bcl)) n = len(X_ctl) ctl_m = X_ctl.mean() ctl_v = X_ctl.var() bcl_m = X_bcl.mean() Z_mean = bcl_m - ctl_m Z_var = bcl_var + ctl_v - 2*np.cov(X_ctl, X_bcl) print(f'Prumer rodilu: {Z_mean}') print(f'Kovariancni matice rozdilu: \n{Z_var}')

#H_0: mean_Z = 0 #H_a: mean != 0 Z_variance = 73464.422 alpha = 0.05 IS_z = calculate_full_ci(Z, None, 'Prumer rozdilu', alpha, logs=True) print('Hypotezu H_0 odmitame.')