def binomial_lln(sample_size, p):
######
## Step 1 - create sample of independent uniform random variables
lower_bound = 0.
upper_bound = 1.
uni_sample = np.random.uniform(lower_bound, upper_bound, sample_size)
######
## Step 2 - transform them to $B(1,p)$ distribution
sample = [dist.binomial_inverse_cdf(p, u) for u in uni_sample]
x_ax = [k for k in range(sample_size)] # values on the x axis
n_plots = 2
y_ax = [[0.] * sample_size for j in range(n_plots)]
# y_values (1) - actual average
y_ax[1] = [p for x in range(sample_size)]
# y_values (0) - cumulative average of all the samples
y_ax[0] = [sum(sample[0:k + 1]) / (k + 1) for k in range(sample_size)]
mp = pu.PlotUtilities("Cumulative Average", 'x', 'Average')
mp.multiPlot(x_ax, y_ax)
def binomial_lln_hist(sample_size, repeats, p):
### plot histogram of Average value of normalised Binomial Distributions
sample_value = [0.] * repeats
num_bins = 35
for i in range(repeats):
######
## Step 1 - create sample of independent uniform random variables
lower_bound = 0.
upper_bound = 1.
uni_sample = np.random.uniform(lower_bound, upper_bound, sample_size)
######
## Step 2 - transform them to $B(1,p)$ distribution
sample = [dist.binomial_inverse_cdf(p, u) for u in uni_sample]
sample_value[i] = (sum(sample) - sample_size * p) / np.sqrt(
p * (1 - p)) / sample_size
mp = pu.PlotUtilities(
"Histogram of Normalised Binomial Average For Sample of Size={0}".
format(sample_size), 'Outcome', 'Rel. Occurrence')
mp.plotHistogram(sample_value, num_bins)
def binomial_histogram(p, sz):
sample = [dist.binomial_inverse_cdf(p, u) for u in getUniformSample(sz)]
num_bins = 100
hp = pu.PlotUtilities(
"Histogram of Binomial Sample with Success Probability={0}".format(p),
'Outcome', 'Rel. Occurrence')
hp.plotHistogram(sample, num_bins)
def binomial_histogram(p, sz):
lower_bound = 0.
upper_bound = 1.
uni_sample = np.random.uniform(lower_bound, upper_bound, sz)
#######
### transform the uniform sample
#######
sample = range(sz)
for j in range(sz):
sample[j] = dist.binomial_inverse_cdf(p, uni_sample[j])
num_bins = 100
hp = pu.PlotUtilities(
"Histogram of Binomial Sample with Success Probability={0}".format(p),
'Outcome', 'Rel. Occurrence')
hp.plotHistogram(sample, num_bins)
def binomial_clt_hist(sample_size, repeats, p):
### plot histogram of Average value of normalised Binomial Distributions
sample_value = [0.] * repeats
num_bins = 35
for i in range(repeats):
######
## Step 1 - create sample of independent uniform random variables
lower_bound = 0.
upper_bound = 1.
uni_sample = np.random.uniform(lower_bound, upper_bound, sample_size)
######
## Step 2 - transform them to $B(1,p)$ distribution
sample = [dist.binomial_inverse_cdf(p, u) for u in uni_sample]
sample_value[i] = (sum(sample) - sample_size * p) / np.sqrt(
sample_size * p * (1 - p))
plt.xlabel('Outcome')
plt.ylabel('Relative Occurrence')
plt.title(
"Histogram of Normalised Binomial Average For Sample of Size={0}".
format(sample_size))
_n, bins, _hist = plt.hist(sample_value,
num_bins,
normed=True,
facecolor='green',
alpha=0.75)
y = [dist.standard_normal_pdf(b) for b in bins]
plt.plot(bins, y, 'r--')
plt.show()
plt.close()
