均匀分布
- 如图：
- 代码如下：
def uniform(x, a, b):
y = [1 / (b - a) if a <= val and val <= b
else 0 for val in x]
return x, y, np.mean(y), np.std(y)
x = np.arange(-100, 100) # define range of x
for ls in [(-50, 50), (10, 20)]:
a, b = ls[0], ls[1]
x, y, u, s = uniform(x, a, b)
plt.plot(x, y, label=r'$\mu=%.2f,\ \sigma=%.2f$' % (u, s))
plt.legend()
plt.title('均匀分布（连续）')
plt.savefig(image_file_path+'/uniform.jpg')
plt.show()
伯努利分布（离散）
- 如图：
- 代码如下
def bernoulli(p, k):
return p if k else 1 - p
n_experiment = 100
p = 0.6
x = np.arange(n_experiment)
y = []
for _ in range(n_experiment):
pick = bernoulli(p, k=bool(random.getrandbits(1)))
y.append(pick)
u, s = np.mean(y), np.std(y)
plt.scatter(x, y, label=r'$\mu=%.2f,\ \sigma=%.2f$' % (u, s))
plt.legend()
plt.title('伯努利分布（离散）')
plt.savefig(image_file_path+'/bernoulli.png')
plt.show()
二项分布（离散）
-
如图：
-
代码如下：
def const(n, r):
r = min(r, n - r)
numer = reduce(op.mul, range(n, n - r, -1), 1)
denom = reduce(op.mul, range(1, r + 1), 1)
return numer / denom
def binomial(n, p):
q = 1 - p
y = [const(n, k) * (p ** k) * (q ** (n - k)) for k in range(n)]
return y, np.mean(y), np.std(y)
for ls in [(0.5, 20), (0.7, 40), (0.5, 40)]:
p, n_experiment = ls[0], ls[1]
x = np.arange(n_experiment)
y, u, s = binomial(n_experiment, p)
plt.scatter(x, y, label=r'$\mu=%.2f,\ \sigma=%.2f$' % (u, s))
plt.legend()
plt.title('二项分布（离散）')
plt.savefig(image_file_path+'/binomial.png')
plt.show()
多项式分布（离散）
- 如图：
- 代码如下：
def factorial(n):
return reduce(op.mul, range(1, n + 1), 1)
def const(n, a, b, c):
assert a + b + c == n
numer = factorial(n)
denom = factorial(a) * factorial(b) * factorial(c)
return numer / denom
def multinomial(n):
ls = []
for i in range(1, n + 1):
for j in range(i, n + 1):
for k in range(j, n + 1):
if i + j + k == n:
ls.append([i, j, k])
y = [const(n, l[0], l[1], l[2]) for l in ls]
x = np.arange(len(y))
return x, y, np.mean(y), np.std(y)
for n_experiment in [20, 21, 22]:
x, y, u, s = multinomial(n_experiment)
plt.scatter(x, y, label=r'$trial=%d$' % (n_experiment))
plt.legend()
plt.title('多项式分布（离散）')
plt.savefig(image_file_path+'/multinomial.png')
plt.show()
伽马分布（连续）
- 如图：
- 代码如下：
def gamma_function(n):
cal = 1
for i in range(2, n):
cal *= i
return cal
def gamma(x, a, b):
c = (b ** a) / gamma_function(a)
y = c * (x ** (a - 1)) * np.exp(-b * x)
return x, y, np.mean(y), np.std(y)
for ls in [(1, 1), (2, 1), (3, 1), (2, 2)]:
a, b = ls[0], ls[1]
x = np.arange(0, 20, 0.01, dtype=np.float)
x, y, u, s = gamma(x, a=a, b=b)
plt.plot(x, y, label=r'$\mu=%.2f,\ \sigma=%.2f,'
r'\ \alpha=%d,\ \beta=%d$' % (u, s, a, b))
plt.legend()
plt.title('伽马分布（连续）')
plt.savefig(image_file_path+'/gamma.png')
plt.show()
高斯分布（连续）
- 如图：
- 代码如下：
def gaussian(x, n):
u = x.mean()
s = x.std()
# divide [x.min(), x.max()] by n
x = np.linspace(x.min(), x.max(), n)
a = ((x - u) ** 2) / (2 * (s ** 2))
y = 1 / (s * np.sqrt(2 * np.pi)) * np.exp(-a)
return x, y, x.mean(), x.std()
x = np.arange(-100, 100) # define range of x
x, y, u, s = gaussian(x, 10000)
plt.plot(x, y, label=r'$\mu=%.2f,\ \sigma=%.2f$' % (u, s))
plt.legend()
plt.title('高斯分布（连续）')
plt.savefig(image_file_path+'/gaussian.png')
plt.show()
正态分布（连续）
- 如图：
- 代码如下：
def normal(x, n):
u = x.mean()
s = x.std()
# normalization
x = (x - u) / s
# divide [x.min(), x.max()] by n
x = np.linspace(x.min(), x.max(), n)
a = ((x - 0) ** 2) / (2 * (1 ** 2))
y = 1 / (s * np.sqrt(2 * np.pi)) * np.exp(-a)
return x, y, x.mean(), x.std()
x = np.arange(-100, 100) # define range of x
x, y, u, s = normal(x, 10000)
plt.plot(x, y, label=r'$\mu=%.2f,\ \sigma=%.2f$' % (u, s))
plt.legend()
plt.title('正态分布（连续）')
plt.savefig(image_file_path+'/normal.png')
plt.show()
