def test_muller_fit():
variance = 0.1 # given in the ques
rvs = generate_muller_rvs(variance)
number_of_bins = int(1.88 * size(rvs) ** (2/5.0))
integrand = lambda x : stats.norm.pdf(x, scale=variance)
writer.append('testing box-muller')
gof.do_chi(rvs, number_of_bins, integrand)
def test_muller_fit():
variance = 0.1 # given in the ques
rvs = generate_muller_rvs(variance)
number_of_bins = int(1.88 * size(rvs)**(2 / 5.0))
integrand = lambda x: stats.norm.pdf(x, scale=variance)
writer.append('testing box-muller')
gof.do_chi(rvs, number_of_bins, integrand)
def run_problem1(sample_size):
u = zeros([sample_size,1])
u = [random.random() for u in u]
f_x = [-1 * log(1-u) for u in u]
g_x = [cos(f_x) for f_x in f_x]
mu = mean(g_x)
writer.append("problem 1 mean is "+str(mu))
def run_problem1(sample_size):
u = zeros([sample_size, 1])
u = [random.random() for u in u]
f_x = [-1 * log(1 - u) for u in u]
g_x = [cos(f_x) for f_x in f_x]
mu = mean(g_x)
writer.append("problem 1 mean is " + str(mu))
def test_gamma_fit():
shape = 5 #given from hw1
rvs = generate_gamma_rvs(shape)
number_of_bins = int(1.88 * size(rvs)**(2 / 5.0))
integrand = lambda x: stats.gamma(5).pdf(x)
writer.append('testing gamma distribution')
gof.do_chi(rvs, number_of_bins, integrand)
def test_cauchy_fit(sample_size):
rvs = generate_cauchy_rvs(sample_size)
number_of_bins = int(1.88 * size(rvs)**(2 / 5.0))
integrand = lambda x: stats.gamma(5).pdf(
x) #cauchy was derived from gamma through the rejection method
writer.append('testing cauchy distribution with ' + str(sample_size) +
' samples')
gof.do_chi(rvs, number_of_bins, integrand)
def run_problem2(sample_size):
u = zeros([sample_size, 1])
u = [random.random() for u in u]
#u = [stats.norm.rvs() for u in u] #not sure whether to use normal or uniform rv
f_x = [arccos((1 - u) - 1 / float(2 * pi)) for u in u]
#f_x = [arccos(2*pi*(1-u)-1) for u in u] #not sure about the equation either - arccos evaluates to nan i.e., undefined
g_x = [2 * pi * ((1 + cos(f_x))**(-2 / float(3))) for f_x in f_x]
mu = mean(g_x)
writer.append("problem 2 mean is " + str(mu))
def run_problem2(sample_size):
u = zeros([sample_size, 1])
u = [random.random() for u in u]
#u = [stats.norm.rvs() for u in u] #not sure whether to use normal or uniform rv
f_x = [arccos((1-u)-1/float(2*pi)) for u in u]
#f_x = [arccos(2*pi*(1-u)-1) for u in u] #not sure about the equation either - arccos evaluates to nan i.e., undefined
g_x = [2*pi*((1+cos(f_x))**(-2/float(3))) for f_x in f_x]
mu = mean(g_x)
writer.append("problem 2 mean is "+str(mu))
def main():
r = zeros((1e6,3))
for i in range(r.shape[0]):
for j in range(r.shape[1]):
r[i,j] = random.exponential()
c1 = r[:,0] + 2*r[:,1] + 3*r[:,2]
# ques a
id_a = c1 > 15
#ques b
id_b= c1 < 1
out_a = r[id_a, 0] + 2*r[id_a, 1] + 3*r[id_a, 2]
out_b = r[id_b, 0] + 2*r[id_b, 1] + 3*r[id_b, 2]
writer.write('')
writer.append('a: '+str(mean(out_a)))
writer.append('b: '+str(mean(out_b)))
def main():
print 'Brewing numbers... '
writer.write('GOODNESS OF FIT TEST FOR FIVE DISTRIBUTIONS\n')
goodness_of_fit_lcg.main()#question 1
writer.append('\n')
goodness_of_fit_rand.main()#question 2
writer.append('\n')
goodness_of_fit_boxmuller.main()#question 3
writer.append('\n')
goodness_of_fit_cauchy.main()#question 4
writer.append('\n')
goodness_of_fit_gamma.main()#question 5
print 'Done. Results written to result/result.txt'
def compare_chisquare(actual, expected):
writer.append('chisquared - actual: ' + str(actual) + ' expected: ' +
str(expected))
if actual <= expected:
writer.append('Accept null hypothesis i.e., good fit')
else:
writer.append('Reject null hypothesis i.e., bad fit')
def test_random_fit():
rvs = generate_random_rvs()
number_of_bins = int(1.88 * size(rvs)**(2 / 5.0))
integrand = lambda x: 1 #pdf for uniform rv
writer.append('testing random')
gof.do_chi(rvs, number_of_bins, integrand)
def main():
test_cauchy_fit(1000)
writer.append('\n')
test_cauchy_fit(10000)
def compare_chisquare(actual, expected):
writer.append('chisquared - actual: '+str(actual)+' expected: '+ str(expected))
if actual <= expected:
writer.append('Accept null hypothesis i.e., good fit')
else:
writer.append('Reject null hypothesis i.e., bad fit')
def calculate_stats(rvs):
writer.append('mean: ' + str(mean(rvs)) + ' variance: ' + str(var(rvs)))
def main():
likelihood = rnd_multi_walk(100)
writer.append("random walk likelihood is " + str(likelihood))
def main():
likelihood = rnd_multi_walk(100)
writer.append("random walk likelihood is "+str(likelihood))
def test_lcg_fit():
rvs = generate_lcg_rvs()
number_of_bins = int(1.88 * size(rvs) ** (2/5.0))
integrand = lambda x : 1 #pdf for uniform rv
writer.append('testing lcg')
gof.do_chi(rvs, number_of_bins, integrand)
def test_cauchy_fit(sample_size):
rvs = generate_cauchy_rvs(sample_size)
number_of_bins = int(1.88 * size(rvs) ** (2/5.0))
integrand = lambda x : stats.gamma(5).pdf(x) #cauchy was derived from gamma through the rejection method
writer.append('testing cauchy distribution with '+str(sample_size)+' samples')
gof.do_chi(rvs, number_of_bins, integrand)
def main():
test_cauchy_fit(1000)
writer.append('\n')
test_cauchy_fit(10000)
def calculate_stats(rvs):
writer.append('mean: '+str(mean(rvs))+' variance: '+str(var(rvs)))
