一些數學分佈的python展示

1、beta分佈

import numpy as np
import matplotlib.pylab as plt
from scipy.stats import beta

if __name__ == '__main__':
    a = 0.5
    b = 0.5
    x = np.arange(0.01, 1, 0.01)
    y = beta.pdf(x, a, b)
    plt.plot(x, y)
    plt.show()

2、指數分佈

import numpy as np
import matplotlib.pylab as plt
from scipy import stats
from scipy.stats import norm

if __name__ == '__main__':
    lambd = 0.5
    x = np.arange(0.1, 15, 0.1) + 0.001
    # y = np.exp(-lambd * x) * lambd + 0.001
    # print(y)
    # Y = np.log(np.array(y))
    # plt.figure(figsize=(10, 5))
    # plt.scatter(x, Y)
    # plt.plot(x, np.log(lambd) - lambd * x, '--')
    # plt.xlim([0, 15])
    y = 1 - np.exp(-lambd * x)
    Y = -np.log(np.array(y))
    plt.scatter(x, Y)
    plt.plot(x, -np.log(1 - np.exp(-lambd * x)), '--')
    plt.show()

3、正態分佈

import numpy as np
import matplotlib.pylab as plt
from scipy.stats import norm

if __name__ == '__main__':
    mu = 0
    sigma = 1
    x = np.arange(-5, 5, 0.1)
    print(len(x))
    y = (sigma * pow(2 * np.pi, 0.5)) ** (-1) * np.exp((-1) * (2 * pow(sigma, 2)) ** (-1) * pow(x - mu, 2)) + 0.000001
    plt.scatter(x, y)
    # Y = np.log(np.array(y))
    # print(Y)
    # plt.scatter(x, Y)
    # plt.plot(x, -1 * np.log(sigma * pow(2 * np.pi, 0.5)) + (-1) * (2 * pow(sigma, 2)) ** (-1) * pow(x - mu, 2), '-')
    # y = norm.pdf(x, 0, 1)
    plt.show()

4、泊松分佈

import numpy as np
import scipy.stats as st
import matplotlib.pyplot as plt

num_years = [4, 10, 7, 5, 4, 0, 0, 1]
lmbda = sum(x * y for x, y in zip(range(8), num_years)) / sum(num_years)
print(lmbda)
rv = st.poisson(lmbda)
x = range(8)
plt.bar(np.array(x), num_years)
plt.plot(x, sum(num_years) * rv.pmf(x), c='r', label='Poisson')
plt.xlim([-1, 8])
plt.ylim([0, 11])
plt.legend(loc='best')
plt.show()

5、冪律分佈

import matplotlib.pyplot as plt
import numpy as np
from sklearn import linear_model
from scipy.stats import norm


def DataGenerate():
    X = np.arange(10, 1010, 10)
    noise = norm.rvs(0, size=100, scale=0.2)
    Y = []
    for i in range(len(X)):
        Y.append(10.8 * pow(X[i], -0.3) + noise[i])

        # plot raw data
    Y = np.array(Y)
    # plt.title("Raw data")
    # plt.scatter(X, Y, color='b')
    # plt.show()

    X0 = np.log10(X)
    Y0 = np.log10(Y)
    return X, Y, X0, Y0


def DataFitAndVisualization(X, Y):
    X_parameter = []
    Y_parameter = []
    for single_square_feet, single_price_value in zip(X, Y):
        X_parameter.append([float(single_square_feet)])
        Y_parameter.append(float(single_price_value))

    regr = linear_model.LinearRegression()  # 一元邏輯迴歸
    # 獲取到參數，畫直線
    print(X_parameter, Y_parameter)
    regr.fit(X_parameter, Y_parameter)
    C = 10 ** regr.intercept_
    print(C)
    r = regr.coef_
    print('Coefficients: \n', regr.coef_)
    print("Intercept:\n", regr.intercept_)
    # The mean square error
    print("Residual sum of squares: %.8f"
          % np.mean((regr.predict(X_parameter) - Y_parameter) ** 2))

    plt.title("Log Data")
    plt.scatter(X_parameter, Y_parameter, color='black')
    plt.plot(X_parameter, regr.predict(X_parameter), color='blue', linewidth=3)

    # plt.xticks(())
    # plt.yticks(())
    plt.show()
    return C, r


if __name__ == "__main__":
    X, Y, X0, Y0 = DataGenerate()
    C, r = DataFitAndVisualization(X0, Y0)
    print(C, X.shape, r.shape) # 10.6884732354 (100,) (1,)
    plt.scatter(X, Y, color='blue')
    plt.plot(X, C * X ** r, color='red', linewidth=1.0, linestyle='-')
    plt.show()