def experiment_2(n_trials, N, n_samples_range):
distance_array = np.empty((n_samples_range + 1, ))
TRUE_VAR = 1
for n in range(2, n_samples_range + 1):
print('Count epoch #: ', n)
total_var, total_var_bag = np.empty(n_trials, ), np.empty(n_trials, )
for i in range(n_trials):
if i % 1000 == 0:
print('Count trial #: ', i)
# x = np.random.normal(0, 1, size=n)
# x = np.random.uniform(-1, 1, size=n)
x = semicircular.rvs(size=n)
# rademacher
# x = 2 * bernouilli - 1
# # Estimator MSE var
var_x = (len(x) / (len(x) - 1)) * np.var(x)
total_var[i] = var_x
# Estimator MSE var avec bagging
mean_bagg = np.empty(N, )
for j in range(N):
bag = bagging_np(x)
var_x_bag = (len(bag) / (len(bag) - 1)) * np.var(bag)
mean_bagg[j] = var_x_bag
var_bag = np.mean(mean_bagg)
total_var_bag[i] = var_bag
EXP_var = np.mean(total_var)
EXP_var_bag = np.mean(total_var_bag)
BIAS_sq_var = (EXP_var - TRUE_VAR)**2
BIAS_sq_var_bag = (EXP_var_bag - TRUE_VAR)**2
VAR_VAR_bag = (len(total_var_bag) /
(len(total_var_bag) - 1)) * np.var(total_var_bag)
VAR_VAR = (len(total_var) / (len(total_var) - 1)) * np.var(total_var)
MSE_VAR = VAR_VAR + BIAS_sq_var
MSE_VAR_BAG = VAR_VAR_bag + BIAS_sq_var_bag
DIST = (MSE_VAR_BAG - MSE_VAR)
distance_array[n] = DIST
return distance_array
def mutation(pop, U, n, mut):
"""
This function creates mutations
"""
###############
# max mutations a poisson number (U is expected number) - MUCH SLOWER!
###############
# nnewmuts = np.random.poisson(U, len(pop)) #poisson number of new mutations for each individual
# oldmuts = np.sum(pop, axis=1) - 1 #number of mutations (not counting origin mutation) already in each individual (from ancestors)
# totmuts = nnewmuts + oldmuts #total number of mutations in each individual
# rtotmuts = np.clip(totmuts, 0, mutmax) #realized total number of mutations: allow each individual to have some max number of mutations
# rnnewmuts = np.clip(rtotmuts - oldmuts, 0, None) #realized number of new mutations
# newmutpop = np.repeat(np.transpose(np.identity(len(pop), dtype=int)), rnnewmuts, axis=1) #columns for new mutations in pop
# pop = np.append(pop, newmutpop, axis=1) #append new columns to population matrix
# newmuts = np.random.multivariate_normal(mean_mut, cov_mut, sum(rnnewmuts)) #phenotypic effect of new mutations
# mut = np.append(mut, newmuts, axis=0) #append effect of new mutations to mutation matrix
###############
# max one new mutation per individual (U is a probability) - MUCH FASTER!
###############
rand3 = np.random.uniform(size=len(
pop)) #random uniform number in [0,1] for each potential mutant
nmuts = sum(
rand3 < U
) # mutate if random number is below mutation probability; returns number of new mutations
whomuts = np.where(rand3 < U) #indices of mutants
newmuts = semicircular.rvs(loc=0,
scale=(4 * l)**0.5, size=n * nmuts).reshape(
nmuts,
n) #phenotypic effect of new mutations
pop = np.append(pop,
np.transpose(np.identity(len(pop), dtype=int)[whomuts[0]]),
axis=1) #add new loci and identify mutants
mut = np.append(mut, newmuts,
axis=0) #append effect of new mutations to mutation list
###############
return [pop, mut]
semicircular.pdf(x),
'r-',
lw=5,
alpha=0.6,
label='semicircular 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 = semicircular()
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = semicircular.ppf([0.001, 0.5, 0.999])
np.allclose([0.001, 0.5, 0.999], semicircular.cdf(vals))
# True
# Generate random numbers:
r = semicircular.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()
plt.title("Experiment 4: Histogram for sums of generated random variables")
plt.hist(samples4, 100, density=True)
# initializations for theoretical normal distribution curve
mu = np.mean(samples4)
sigma = np.std(samples4)
x = np.linspace(mu - 6*sigma, mu + 6*sigma, 200)
plt.plot(x, stats.norm.pdf(x, mu, sigma))
plt.show()
# * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
# Experiment 5:
s = semicircular.rvs(2, 1, size=50000) # 50000 randomly generated values from a distribution of semi-circle of radius 1 centered at 2.
samples5 = [np.sum(random.choices(s, k=2)) for i in range(50000)] # Number of values is 2.
print("Experiment 5: ")
print("Sample mean is ", np.mean(samples5))
print("Sample standard deviation is ", np.std(samples5))
plt.figure()
plt.title("Experiment 5: Histogram for generated random variables")
plt.hist(s, 100, density=True)
plt.show()
plt.title("Experiment 5: Histogram for sums of generated random variables")
plt.hist(samples5, 100, density=True)
# initializations for theoretical normal distribution curve
mu = np.mean(samples5)
sigma = np.std(samples5)
plt.title("Histogram for generated random variables")
plt.hist(bigs, 70, cumulative=0, density=True)
plt.show()
plt.figure()
plt.title("Histogram for sums of generated random variables")
plt.hist(total, 70, cumulative=0, density=True)
mu = np.mean(total)
sigma = np.std(total)
x = np.linspace(mu - 8 * sigma, mu + 8 * sigma, 4000)
plt.plot(x, stats.norm.pdf(x, mu, sigma))
plt.show()
print("\n--------------------------\n")
#Experiment 5-6-7
for values in LOV:
s = semicircular.rvs(2, 1, 10000)
total = []
for i in range(4000):
total.append(sum(random.choices(s, k=values)))
print("Sample mean is:", np.mean(total))
print("Sample standart deviation is:", np.std(total))
plt.figure()
plt.title("Histogram for generated random variables")
plt.hist(s, 70, cumulative=0, density=True)
plt.show()
plt.figure()
plt.title("Histogram for sums of generated random variables")
plt.hist(total, 50, cumulative=0, density=True)
mu = np.mean(total)
sigma = np.std(total)
x = np.linspace(mu - 8 * sigma, mu + 8 * sigma, 4000)
import math
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import bernoulli
from scipy.stats import norm
from scipy.stats import binom
from scipy.stats import semicircular
#number of test cases for each variable
k = 10000
#counter for counting the number of times favourable situation occurs
count = 0
#creating an array of x coordinate using semicircular function
data_x = semicircular.rvs(loc=0, scale=1, size=k, random_state=None)
#creating an array of x coordinate using semicircular function
data_y = semicircular.rvs(loc=0, scale=1, size=k, random_state=None)
#comparing each term of both arrays and counting number of times the favourable situation occurs
for i in range(k):
for j in range(k):
#print(" " + str(data_y[j]) + ":" + str(data_x[i]))
if (data_y[j] > abs(data_x[i])):
count = count + 1
#probability of the event is number of times the situation occured / total test cases
# total test cases is k^2
probab = count / pow(k, 2)
print("The probability is: ", probab)