Python如何检验样本是否服从正态分布

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
 
# 使用pandas和numpy生成一组仿真数据
s = pd.DataFrame(np.random.randn(500),columns=['value'])
print(s.shape)      # (500, 1)
 
# 创建自定义图像
fig = plt.figure(figsize=(10, 6))
# 创建子图1
ax1 = fig.add_subplot(2,1,1)
# 绘制散点图
ax1.scatter(s.index, s.values)
plt.grid()      # 添加网格
 
# 创建子图2
ax2 = fig.add_subplot(2, 1, 2)
# 绘制直方图
s.hist(bins=30,alpha=0.5,ax=ax2)
# 绘制密度图
s.plot(kind='kde', secondary_y=True,ax=ax2)     # 使用双坐标轴
plt.grid()      # 添加网格
 
# 显示自定义图像
plt.show()

def kstest(rvs, cdf, args=(), N=20, alternative='two-sided', mode='approx'):
    """
    Perform the Kolmogorov-Smirnov test for goodness of fit.
    This performs a test of the distribution F(x) of an observed
    random variable against a given distribution G(x). Under the null
    hypothesis the two distributions are identical, F(x)=G(x). The
    alternative hypothesis can be either 'two-sided' (default), 'less'
    or 'greater'. The KS test is only valid for continuous distributions.
    Parameters
    ----------
    rvs : str, array or callable
        If a string, it should be the name of a distribution in `scipy.stats`.
        If an array, it should be a 1-D array of observations of random
        variables.
        If a callable, it should be a function to generate random variables;
        it is required to have a keyword argument `size`.
    cdf : str or callable
        If a string, it should be the name of a distribution in `scipy.stats`.
        If `rvs` is a string then `cdf` can be False or the same as `rvs`.
        If a callable, that callable is used to calculate the cdf.
    args : tuple, sequence, optional
        Distribution parameters, used if `rvs` or `cdf` are strings.
    N : int, optional
        Sample size if `rvs` is string or callable.  Default is 20.
    alternative : {'two-sided', 'less','greater'}, optional
        Defines the alternative hypothesis (see explanation above).
        Default is 'two-sided'.
    mode : 'approx' (default) or 'asymp', optional
        Defines the distribution used for calculating the p-value.
          - 'approx' : use approximation to exact distribution of test statistic
          - 'asymp' : use asymptotic distribution of test statistic
    Returns
    -------
    statistic : float
        KS test statistic, either D, D+ or D-.
    pvalue :  float
        One-tailed or two-tailed p-value.

def normaltest(a, axis=0, nan_policy='propagate'):
    """
    Test whether a sample differs from a normal distribution.
    This function tests the null hypothesis that a sample comes
    from a normal distribution.  It is based on D'Agostino and
    Pearson's [1]_, [2]_ test that combines skew and kurtosis to
    produce an omnibus test of normality.
    Parameters
    ----------
    a : array_like
        The array containing the sample to be tested.
    axis : int or None, optional
        Axis along which to compute test. Default is 0. If None,
        compute over the whole array `a`.
    nan_policy : {'propagate', 'raise', 'omit'}, optional
        Defines how to handle when input contains nan. 'propagate' returns nan,
        'raise' throws an error, 'omit' performs the calculations ignoring nan
        values. Default is 'propagate'.
    Returns
    -------
    statistic : float or array
        ``s^2 + k^2``, where ``s`` is the z-score returned by `skewtest` and
        ``k`` is the z-score returned by `kurtosistest`.
    pvalue : float or array
       A 2-sided chi squared probability for the hypothesis test.

def shapiro(x):
    """
    Perform the Shapiro-Wilk test for normality.
    The Shapiro-Wilk test tests the null hypothesis that the
    data was drawn from a normal distribution.
    Parameters
    ----------
    x : array_like
        Array of sample data.
    Returns
    -------
    W : float
        The test statistic.
    p-value : float
        The p-value for the hypothesis test.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
 
# 使用pandas和numpy生成一组仿真数据
s = pd.DataFrame(np.random.randn(500),columns=['value'])
print(s.shape)      # (500, 1)
 
# 计算均值
u = s['value'].mean()
# 计算标准差
std = s['value'].std()  # 计算标准差
print('scipy.stats.kstest统计检验结果：----------------------------------------------------')
print(stats.kstest(s['value'], 'norm', (u, std)))
print('scipy.stats.normaltest统计检验结果：----------------------------------------------------')
print(stats.normaltest(s['value']))
print('scipy.stats.shapiro统计检验结果：----------------------------------------------------')
print(stats.shapiro(s['value']))