def base_digit_reality(cell, base = None, digit = None, total_wanted = None):
if base is None:
base = cell.base
if digit is None:
digit = cell.digit
if total_wanted is None:
total_wanted = cell.total_wanted
base = float(base)
digit = float(digit)
k = float(total_wanted)
total_possible_way = base**digit
binomial_coefficient = float(alva.productA(digit)) / (alva.productA(k) * alva.productA(digit - k))
total_work_way = binomial_coefficient * (base - 1)**(digit - k)
probability = total_work_way / total_possible_way
return (probability)
def base_digit_reality(cell, base = None, digit = None, total_wanted = None):
if base is None:
base = cell.base
if digit is None:
digit = cell.digit
if total_wanted is None:
total_wanted = cell.total_wanted
base = float(base)
digit = float(digit)
k = float(total_wanted)
total_possible_way = base**digit
binomial_coefficient = float(alva.productA(digit)) / (alva.productA(k) * alva.productA(digit - k))
total_work_way = binomial_coefficient * (base - 1)**(digit - k)
probability = total_work_way / total_possible_way
return (probability)
def AlvaBinomialD(i, N, p):
B_distribution = 0.0*i
B_distribution[:] = alva.productA(N) / (alva.productA(i[:]) * alva.productA(N - i[:])) * p**i[:] * (1 - p)**(N - i[:])
return (B_distribution)
plt.title(r'$ Binomial-distribution---probability-mass-function $',fontsize = AlvaFontSize)
plt.text(0, 5.0/6, r'$ P(n|N) = \frac{N!}{n!(N - n)!} p^n (1 - p)^{N - n} $', fontsize = 1.2*AlvaFontSize)
plt.text(0, 4.0/6, r'$ 1-- \ a \ set \ of \ N \ events $', fontsize = AlvaFontSize)
plt.text(0, 3.0/6, r'$ 2-- \ either \ Success \ or \ Failure \ for \ each \ event $', fontsize = AlvaFontSize)
plt.text(0, 2.0/6, r'$ 3-- \ the \ probability-p \ is \ the \ same \ for \ all \ events $', fontsize = AlvaFontSize)
plt.text(0, 1.0/6, r'$ 4-- \ P(n|N) \ is \ the \ probability \ with \ n-success \ events \ in \ a \ total \ of \ N \ events $',
fontsize = AlvaFontSize)
plt.savefig(save_figure, dpi = 300)
plt.show()
# In[3]:
#testing
i = 100
print ('AlvaM =', alva.productA(i))
print ('NumPy =', np.arange(1, i + 1).prod(dtype = float))
def AlvaBinomialD(i, N, p):
B_distribution = 0.0*i
B_distribution[:] = alva.productA(N) / (alva.productA(i[:]) * alva.productA(N - i[:])) * p**i[:] * (1 - p)**(N - i[:])
return (B_distribution)
def AlvaBinomialC(m, N, p, binomialD):
B_C = 0.0*m
for j in range(np.size(m)):
for k in range(m[j]):
i = np.arange(k + 1)
B_distribution = binomialD(i, N, p)
B_C[j] = B_C[j] + B_distribution.sum()
def AlvaBinomialD(i, N, p):
B_distribution = 0.0 * i
B_distribution[:] = alva.productA(N) / (alva.productA(
i[:]) * alva.productA(N - i[:])) * p**i[:] * (1 - p)**(N - i[:])
return (B_distribution)
2.0 / 6,
r'$ 3-- \ the \ probability-p \ is \ the \ same \ for \ all \ events $',
fontsize=AlvaFontSize)
plt.text(
0,
1.0 / 6,
r'$ 4-- \ P(n|N) \ is \ the \ probability \ with \ n-success \ events \ in \ a \ total \ of \ N \ events $',
fontsize=AlvaFontSize)
plt.savefig(save_figure, dpi=300)
plt.show()
# In[3]:
#testing
i = 100
print('AlvaM =', alva.productA(i))
print('NumPy =', np.arange(1, i + 1).prod(dtype=float))
def AlvaBinomialD(i, N, p):
B_distribution = 0.0 * i
B_distribution[:] = alva.productA(N) / (alva.productA(
i[:]) * alva.productA(N - i[:])) * p**i[:] * (1 - p)**(N - i[:])
return (B_distribution)
def AlvaBinomialC(m, N, p, binomialD):
B_C = 0.0 * m
for j in range(np.size(m)):
for k in range(m[j]):
i = np.arange(k + 1)
def binomialPMF(total_event, p):
x_event = np.arange(1, total_event + 1)
y_PMF = alva.productA(total_event) / (alva.productA(x_event) * alva.productA(total_event - x_event)) * p**x_event * (1 - p)**(total_event - x_event)
return np.array([x_event, y_PMF])