xs = range(4, x + 1)
probs = list()
for x in xs:
prob = stats.nbinom.pmf(x - r, r, p)
probs.append(round(prob, 8))
print('{0}The probability that E occurs exactly {1} times by the {2}th event is {3:.8}'\
.format(space, r, x, prob))
# ----------------------------------------
# plotting
# ----------------------------------------
xs = np.array(xs)
probs = np.array(probs).round(4)
plots.barplot(xs, probs
,title = 'Negative Binomial Distribution; p = {0:.8}, r = {1}'\
.format(pplot, rplot)
,align = 'edge'
,edgecolor = edgecolor
,show = False, close = False)
# ----------------------------------------
# cumulative probabilities
# ----------------------------------------
x = 5
r = 3
p = 0.2
print('')
print('{0}An event E occurs with a probability of {1}.'.format(space, p))
prob = 0
xs = range(r, x + 1)
for x in xs:
prob = prob + stats.nbinom.pmf(x - r, r, p)
# Calculate rating means of random movies
(means, stddevs, processed_titles) = means_of_random_movies(args.n, twitter_search_type=args.t,
top_movies_only=args.top_movies_only,
tweet_threshold=args.threshold)
# Unpack scores
tw_means, tw_stddevs = means, stddevs
# Get netflix ratings
netflix_scores = map(nf_title_score, processed_titles)
nf_means, nf_stddevs = zip(*netflix_scores)
correlation_coefficient = correlation(tw_means, nf_means)
if DEBUG:
print "Twitter stddev: %.2f" % stddev(tw_means)
print "Netflix stddev: %.2f" % stddev(nf_means)
print "Correlation: %.2f" % correlation_coefficient
if args.normalize:
mean_diff = average(nf_means) - average(tw_means)
print "Adjusting twitter means by %.2f (nf avg mean: %.2f; tw avg mean: %.2f)" % (mean_diff, average(nf_means), average(tw_means))
tw_means = map(lambda mean: mean + mean_diff, tw_means)
if args.plot:
data = (tw_means, nf_means)
errors = (tw_stddevs, nf_stddevs) if args.show_errors else None
xlabels = map(initials, processed_titles)
plt = barplot(data, errors=errors, xlabels=xlabels)
plt.show()
xs = np.arange(mu - 5, mu + 5 + 1, (mu / 10))
for xl in xs:
pdfval = stats.norm.pdf(xl, mu, sigma)
pdfvals.append(pdfval)
print('{0}The value of the probability density function at x = {1} is {2:.8}.'\
.format(space, xl, pdfval))
# ----------------------------------------
# plotting
# ----------------------------------------
xs = np.array(xs)
pdfvals = np.array(pdfvals).round(4)
plots.barplot(xs,
pdfvals,
title='Normal Distribution; mu = {0:.8}, sigma = {1}'.format(
mu, sigma),
align='edge',
edgecolor=edgecolor,
show=False,
close=False)
print('')
# ----------------------------------------
# cumulative probabilities
# ----------------------------------------
x = 7
h = 1e-6
probcum = stats.norm.cdf(x, mu, sigma)
xs = np.arange((int)(-6 * sigma), x, h)
probs = stats.norm.pdf(xs, mu, sigma)
probcum2 = probs * h
probcum2 = probcum2.sum()
.format(space, x, pdfval))
pdfvals = list()
xstart = (float)(0.02)
xend = (float)(0.7)
h = (float)(0.02)
xs = np.arange(xstart, xend, h)
pdfvals = stats.expon.pdf(xs, 0, 1 / lamb).round(8)
# ----------------------------------------
# plotting
# ----------------------------------------
xs = np.array(xs).round(4)
pdfvals = np.array(pdfvals).round(2)
fig, ax1 = plots.barplot(xs, pdfvals
,title = 'Exponential Distribution; lambda = {0:.8}'.format(lamb)
,align = 'edge'
,edgecolor = edgecolor
,width = h
,show = False, close = False)
ax2 = ax1.twinx()
fig, ax2 = plots.scatter(xs, pdfvals, fig = fig, ax = ax1
,ylim = ax1.get_ylim(), markersize = 0, linewidth = 2)
ax2.set_title('')
# ----------------------------------------
# sample calculations 1
# ----------------------------------------
prob1 = stats.expon.cdf(x, 0, 1 / lamb)
prob1calc = 1 - math.exp(-x * lamb)
prob2 = 1 - prob1
assert(0.082 - round(prob2, 3) == 0)
assert(round(prob1 - prob1calc, 8) == 0)
xs = range(0, n + 1)
for x in xs:
prob = stats.binom.pmf(x, n, p)
probs.append(round(prob, 8))
print('{0}The probability that E occurs {1} times'.format(space, x) +\
' in the next {0} events is {1:.8}.'.format(n, prob))
# ----------------------------------------
# plotting
# ----------------------------------------
xs = np.array(xs)
probs = np.array(probs).round(4)
plots.barplot(xs,
probs,
title='Binomial Distribution; p = {0:.8}, n = {1}'.format(
p, n),
align='edge',
edgecolor=edgecolor,
show=False,
close=False)
print('')
# ----------------------------------------
# cumulative probabilities
# ----------------------------------------
x = 4
prob = 0
probcum = stats.binom.cdf(x - 1, n, p)
probcum = 1 - probcum
for x in range(0, x):
prob = prob + stats.binom.pmf(x, n, p)
prob = 1 - prob
xs = range(0, x + 5)
for xl in xs:
prob = stats.poisson.pmf(xl, lamb * T)
probs.append(prob)
print('{0}The probability that E occurs {1} times'.format(space, xl) +\
' in T = {0} units is {1:.8}'.format(T, prob))
# ----------------------------------------
# plotting
# ----------------------------------------
xs = np.array(xs)
probs = np.array(probs).round(4)
plots.barplot(xs,
probs,
title='Poisson Distribution; lamb = {0}, T = {1}'.format(
lamb, T),
align='edge',
edgecolor=edgecolor,
show=False,
close=False)
print('')
# ----------------------------------------
# cumulative probabilities
# ----------------------------------------
x = 1
T = 2
probcum = stats.poisson.cdf(x, lamb * T)
probcum = 1 - probcum + stats.poisson.pmf(x, lamb * T)
prob = 0
for xl in range(0, x):
prob = prob + stats.poisson.pmf(xl, lamb * T)
xs = range(x + 1)
for x in xs:
prob = stats.geom.pmf(x, p)
probs.append(round(prob, 8))
print('{0}The probability that E first occurs in {1} times is {2:.8}'\
.format(space, x, prob))
# ----------------------------------------
# plotting
# ----------------------------------------
xs = np.array(xs)
probs = np.array(probs).round(4)
plots.barplot(xs,
probs,
title='Geometric Distribution; p = {0:.8}'.format(p),
align='edge',
edgecolor=edgecolor,
show=False,
close=False)
print('')
# ----------------------------------------
# cumulative probabilities
# ----------------------------------------
x = 4
prob = 0
for x in range(0, x):
prob = prob + stats.geom.pmf(x, p)
prob = 1 - prob
assert (0.729 == round(prob, 3))
print('{0}The probability that E first occurs in >= {1} events is {2:.8}'.
probs = list()
xs = range(0, n + 1)
for x in xs:
prob = stats.hypergeom.pmf(x, N, K, n)
probs.append(round(prob, 8))
print('{0}The probability that the sample contains x = {1} objects of interest is {2:.8}.'\
.format(space, x, prob))
# ----------------------------------------
# plotting
# ----------------------------------------
xs = np.array(xs)
probs = np.array(probs).round(4)
plots.barplot(xs, probs
,title = 'Hypergeometric Distribution; N = {0}, K = {1}, n = {2}'.format(N, K, n)
,align = 'edge'
,edgecolor = edgecolor
,show = False, close = False)
print('')
# ----------------------------------------
# cumulative probabilities
# ----------------------------------------
N = 300
K = 100
n = 4
x = 2
probcum = stats.hypergeom.cdf(x, N, K, n)
probcum = 1 - probcum + stats.hypergeom.pmf(x, N, K, n)
prob = 0
xs = range(0, x)
twitter_search_type=args.t,
top_movies_only=args.top_movies_only,
tweet_threshold=args.threshold)
# Unpack scores
tw_means, tw_stddevs = means, stddevs
# Get netflix ratings
netflix_scores = map(nf_title_score, processed_titles)
nf_means, nf_stddevs = zip(*netflix_scores)
correlation_coefficient = correlation(tw_means, nf_means)
if DEBUG:
print "Twitter stddev: %.2f" % stddev(tw_means)
print "Netflix stddev: %.2f" % stddev(nf_means)
print "Correlation: %.2f" % correlation_coefficient
if args.normalize:
mean_diff = average(nf_means) - average(tw_means)
print "Adjusting twitter means by %.2f (nf avg mean: %.2f; tw avg mean: %.2f)" % (
mean_diff, average(nf_means), average(tw_means))
tw_means = map(lambda mean: mean + mean_diff, tw_means)
if args.plot:
data = (tw_means, nf_means)
errors = (tw_stddevs, nf_stddevs) if args.show_errors else None
xlabels = map(initials, processed_titles)
plt = barplot(data, errors=errors, xlabels=xlabels)
plt.show()
n = 10 # in this many trials
x1 = 0
x2 = 10
probs = list()
xs1 = np.array(range(x1, x2 + 1))
probs = stats.binom.pmf(xs1, n, p)
xs2 = np.arange(x1, x2, 1e-1)
proba = stats.norm.pdf((xs2 - (n * p))/(math.sqrt((n * p) * (1 - p))))
# ----------------------------------------
# plotting
# ----------------------------------------
probs = np.array(probs).round(4)
fig, ax1 = plots.barplot(xs1, probs
,title = 'Normal Approximation of Binomial Distribution; p = {0:.8}, n = {1}'.format(p, n)
,align = 'edge'
,edgecolor = edgecolor
,show = False, close = False)
ax2 = ax1.twinx()
fig, ax2 = plots.scatter(xs2 + 0.5, proba, fig = fig, ax = ax2, markersize = 0, linewidth = 2)
ax2.set_title('')
print('')
# ----------------------------------------
# sample calculations
# ----------------------------------------
p = 1e-5 # probability of E occurring
n = 16e6 # in this many trials
x = 150 # contains this many occurrences of E
h = 1 # step size
xs1 = np.arange(0, x + h, 1)