我查看了Best fit Distribution plots问题，发现提交的答案使用 Kolmogorov-Smirnov 检验来找到最佳拟合分布。我还发现有一个 Anderson-Darling 检验也用于获得最佳拟合分布。所以，我有几个问题：
问题一：
如果我有数据并通过 NumPy 直方图传递，我应该使用哪些参数以及应该将哪些输出输入到分布中？
def get_hist(data, data_size):
#### General code:
bins_formulas = ['auto', 'fd', 'scott', 'rice', 'sturges', 'doane', 'sqrt']
# bins = np.histogram_bin_edges(a=data, bins='scott')
# bins = np.histogram_bin_edges(a=data, bins='auto')
bins = np.histogram_bin_edges(a=data, bins='fd')
# print('Bin value = ', bins)
# Obtaining the histogram of data:
# Hist, bin_edges = histogram(a=data, bins=bins, range=np.linspace(start=np.min(data),end=np.max(data),size=data_size), density=True)
# Hist, bin_edges = histogram(a=data, range=np.linspace(np.min(data), np.max(data), data_size), density=True)
# Hist, bin_edges = histogram(a=data, bins=bins, density=True)
# Hist, bin_edges = histogram(a=data, bins=bins, range=(min(data), max(data)), normed=True, density=True)
# Hist, bin_edges = histogram(a=data, density=True)
Hist, bin_edges = histogram(a=data, range=(min(data), max(data)), density=True)
return Hist
问题2：
如果我想结合这两个测试，我该怎么做？哪些参数最适合用于寻找最佳拟合分布？这是我结合这两个测试的尝试。
from statsmodels.stats.diagnostic import anderson_statistic as adtest
def get_best_distribution(data):
dist_names = ['alpha', 'anglit', 'arcsine', 'beta', 'betaprime', 'bradford', 'burr', 'cauchy', 'chi', 'chi2', 'cosine', 'dgamma', 'dweibull', 'erlang', 'expon', 'exponweib', 'exponpow', 'f', 'fatiguelife', 'fisk', 'foldcauchy', 'foldnorm', 'frechet_r', 'frechet_l', 'genlogistic', 'genpareto', 'genexpon', 'genextreme', 'gausshyper', 'gamma', 'gengamma', 'genhalflogistic', 'gilbrat', 'gompertz', 'gumbel_r', 'gumbel_l', 'halfcauchy', 'halflogistic', 'halfnorm', 'hypsecant', 'invgamma', 'invgauss', 'invweibull', 'johnsonsb', 'johnsonsu', 'ksone', 'kstwobign', 'laplace', 'logistic', 'loggamma', 'loglaplace', 'lognorm', 'lomax', 'maxwell', 'mielke', 'moyal', 'nakagami', 'ncx2', 'ncf', 'nct', 'norm', 'pareto', 'pearson3', 'powerlaw', 'powerlognorm', 'powernorm', 'rdist', 'reciprocal', 'rayleigh', 'rice', 'recipinvgauss', 'semicircular', 't', 'triang', 'truncexpon', 'truncnorm', 'tukeylambda', 'uniform', 'vonmises', 'wald', 'weibull_min', 'weibull_max', 'wrapcauchy']
dist_ks_results = []
dist_ad_results = []
params = {}
for dist_name in dist_names:
dist = getattr(st, dist_name)
param = dist.fit(data)
params[dist_name] = param
# Applying the Kolmogorov-Smirnov test
D_ks, p_ks = st.kstest(data, dist_name, args=param)
print("Kolmogorov-Smirnov test Statistics value for " + dist_name + " = " + str(D_ks))
# print("p value for " + dist_name + " = " + str(p_ks))
dist_ks_results.append((dist_name, p_ks))
# Applying the Anderson-Darling test:
D_ad = adtest(x=data, dist=dist, fit=False, params=param)
print("Anderson-Darling test Statistics value for " + dist_name + " = " + str(D_ad))
dist_ad_results.append((dist_name, D_ad))
print(dist_ks_results)
print(dist_ad_results)
for D in range (len(dist_ks_results)):
KS_D = dist_ks_results[D][1]
AD_D = dist_ad_results[D][1]
if KS_D < 0.25 and AD_D < 0.05:
best_ks_D = KS_D
best_ad_D = AD_D
if dist_ks_results[D][1] == best_ks_D:
best_ks_dist = dist_ks_results[D][0]
if dist_ad_results[D][1] == best_ad_D:
best_ad_dist = dist_ad_results[D][0]
print(best_ks_D)
print(best_ad_D)
print(best_ks_dist)
print(best_ad_dist)
print('\n################################ Kolmogorov-Smirnov test parameters #####################################')
print("Best fitting distribution (KS test): " + str(best_ks_dist))
print("Best test Statistics value (KS test): " + str(best_ks_D))
print("Parameters for the best fit (KS test): " + str(params[best_ks_dist])
print('################################################################################\n')
print('################################ Anderson-Darling test parameters #########################################')
print("Best fitting distribution (AD test): " + str(best_ad_dist))
print("Best test Statistics value (AD test): " + str(best_ad_D))
print("Parameters for the best fit (AD test): " + str(params[best_ad_dist]))
print('################################################################################\n')
问题 3：
如何获得 Anderson-Darling 检验的 p 值？
问题4：
假设我设法获得了最佳拟合分布，如何根据测试对分布进行排名？像下面的照片。
编辑 1
我不确定，但来自 statsmodel 的 normal_ad 是针对任何连续概率分布的一般 Anderson-Darling 测试吗？如果是，我想选择两个测试通用的分布，如果我按照问题 1 中的相同步骤进行操作，这是否是正确的方法？另外，假设我想找到最高的 p 值并且在两个测试中都很常见，我如何使用 p 值提取公共分布名称？
def get_best_distribution(data):
dist_names = ['beta', 'bradford', 'burr', 'cauchy', 'chi', 'chi2', 'erlang', 'expon', 'f', 'fatiguelife', 'fisk', 'gamma', 'genlogistic', 'genpareto', 'invgauss', 'johnsonsb', 'johnsonsu', 'laplace', 'logistic', 'loggamma', 'loglaplace', 'lognorm', 'maxwell', 'mielke', 'norm', 'pareto', 'reciprocal', 'rayleigh', 't', 'triang', 'uniform', 'weibull_min', 'weibull_max']
dist_ks_results = []
dist_ad_results = []
params = {}
for dist_name in dist_names:
dist = getattr(st, dist_name)
param = dist.fit(data)
params[dist_name] = param
# Applying the Kolmogorov-Smirnov test
D_ks, p_ks = st.kstest(data, dist_name, args=param)
print("Kolmogorov-Smirnov test Statistics value for " + dist_name + " = " + str(D_ks))
print("p value (KS test) for " + dist_name + " = " + str(p_ks))
dist_ks_results.append((dist_name, p_ks))
# Applying the Anderson-Darling test:
D_ad, p_ad = adnormtest(x=data, axis=0)
print("Anderson-Darling test Statistics value for " + dist_name + " = " + str(D_ad))
print("p value (AD test) for " + dist_name + " = " + str(p_ad))
dist_ad_results.append((dist_name, p_ad))
# select the best fitted distribution:
best_ks_dist, best_ks_p = (max(dist_ks_results, key=lambda item: item[1]))
best_ad_dist, best_ad_p = (max(dist_ad_results, key=lambda item: item[1]))
print('\n################################ Kolmogorov-Smirnov test parameters #####################################')
print("Best fitting distribution (KS test) :" + str(best_ks_dist))
print("Best p value (KS test) :" + str(best_ks_p))
print("Parameters for the best fit (KS test) :" + str(params[best_ks_dist]))
print('###########################################################################################################\n')
print('################################ Anderson-Darling test parameters #########################################')
print("Best fitting distribution (AD test) :" + str(best_ad_dist))
print("Best p value (AD test) :" + str(best_ad_p))
print("Parameters for the best fit (AD test) :" + str(params[best_ad_dist]))
print('###########################################################################################################\n')
if best_ks_dist == best_ad_dist:
best_common_dist = best_ks_dist
print('##################################### Both test parameters ############################################')
print("Best fitting distribution (Both test) :" + str(best_common_dist))
print("Best p value (KS test) :" + str(best_ks_p))
print("Best p value (AD test) :" + str(best_ad_p))
print("Parameters for the best fit (Both test) :" + str(params[best_common_dist]))
print('###########################################################################################################\n')
return best_common_dist, best_ks_p, params[best_common_dist]
问题 5：
如果我在实施拟合优度检验时出错，请纠正我，使用获得的 p 值来检查给定值是否适合任何上述分布。因此，p 值的最大值意味着 p 值低于 %5 显着水平，因此，例如，Gamma 分布拟合数据。我是对的还是我错过了对拟合优度测试的主要概念的理解？