分布图显示平面 pdf

Question

在找到最佳参数后，我试图绘制我的数据的Probability Density Function (PDF) plot，但绘图显示的是一条平线而不是曲线。

• 是缩放问题吗？
• 是Continuous or Discrete data的问题吗？数据文件可用here
• 这里的目的是得到最好的分布拟合，然后绘制 PDF 函数。

• 我的数据值非常小，例如：0.21, 1.117 .etc。数据统计和PDF图如下所示：

我的脚本如下：

from time import time
from datetime import datetime
start_time = datetime.now()
import pandas as pd
pd.options.display.float_format = '{:.4f}'.format
import numpy as np
import pickle
import scipy
import scipy.stats
import matplotlib.pyplot as plt

data= pd.read_csv("line_RXC_data.csv",usecols=['R'],parse_dates=True, squeeze=True)
df=data

y_std=df
# del yy

import warnings
warnings.filterwarnings("ignore")


# Create an index array (x) for data

y=df
#
# Create an index array (x) for data

x = np.arange(len(y))
size = len(y)

#simple visualisation of the data
plt.hist(y)
plt.title("Histogram of resistance ")
plt.xlabel("Resistance data visualization ")
plt.ylabel("Frequency")
plt.show()

y_df = pd.DataFrame(y)
tt=y_df.describe()
print(tt)

dist_names = [
                'foldcauchy',
                'beta',
                'expon',
                  'exponnorm',
                'norm', 
                'lognorm',
                  'dweibull',
                'pareto',
                  'gamma'
]


x = np.arange(len(df))
size = len(df)
y_std = df
y=df
chi_square = []
p_values = []

# Set up 50 bins for chi-square test
# Observed data will be approximately evenly distrubuted aross all bins
percentile_bins = np.linspace(0,100,51)
percentile_cutoffs = np.percentile(y_std, percentile_bins)
observed_frequency, bins = (np.histogram(y_std, bins=percentile_cutoffs))
cum_observed_frequency = np.cumsum(observed_frequency)

# Loop through candidate distributions

for distribution in dist_names:
    s1 = time()
    # Set up distribution and get fitted distribution parameters
    dist = getattr(scipy.stats, distribution)
    # print("1")
    param = dist.fit(y_std)
    # print("2")
    # Obtain the KS test P statistic, round it to 5 decimal places
    p = scipy.stats.kstest(y_std, distribution, args=param)[1]
    p = np.around(p, 5)
    p_values.append(p)    
    # print("3")
    # Get expected counts in percentile bins
    # This is based on a 'cumulative distrubution function' (cdf)
    cdf_fitted = dist.cdf(percentile_cutoffs, *param[:-2], loc=param[-2], 
                          scale=param[-1])
    # print("4")
    expected_frequency = []
    for bin in range(len(percentile_bins)-1):
        expected_cdf_area = cdf_fitted[bin+1] - cdf_fitted[bin]
        expected_frequency.append(expected_cdf_area)

    # calculate chi-squared
    expected_frequency = np.array(expected_frequency) * size
    cum_expected_frequency = np.cumsum(expected_frequency)
    ss = sum (((cum_expected_frequency - cum_observed_frequency) ** 2) / cum_observed_frequency)
    chi_square.append(ss)
    print(f"chi_square {distribution} time: {time() - s1}")

#    print("std of predicted probability : ", np.std(cum_observed_frequency))   

# Collate results and sort by goodness of fit (best at top)

results = pd.DataFrame()
results['Distribution'] = dist_names
results['chi_square'] = chi_square
results['p_value'] = p_values
results.sort_values(['chi_square'], inplace=True)

# Report results

print ('\nDistributions sorted by goodness of fit:')
print ('----------------------------------------')
print (results)


#%%

# Divide the observed data into 100 bins for plotting (this can be changed)
number_of_bins = 100
bin_cutoffs = np.linspace(np.percentile(y,0), np.percentile(y,99),number_of_bins)

# Create the plot
plt.figure(figsize=(7, 4))
h = plt.hist(y, bins = bin_cutoffs, color='0.70')

# Get the top three distributions from the previous phase
number_distributions_to_plot = 5
dist_names = results['Distribution'].iloc[0:number_distributions_to_plot]


#%%
# Create an empty list to stroe fitted distribution parameters
parameters = []

# Loop through the distributions ot get line fit and paraemters

for dist_name in dist_names:
    # Set up distribution and store distribution paraemters
    dist = getattr(scipy.stats, dist_name)
    param = dist.fit(y)
    parameters.append(param)

    # Get line for each distribution (and scale to match observed data)
    pdf_fitted = dist.pdf(x, *param[:-2], loc=param[-2], scale=param[-1])
    scale_pdf = np.trapz (h[0], h[1][:-1]) / np.trapz (pdf_fitted, x)
    pdf_fitted *= scale_pdf

    # Add the line to the plot
    plt.plot(pdf_fitted, label=dist_name)

    # Set the plot x axis to contain 99% of the data
    # This can be removed, but sometimes outlier data makes the plot less clear
    plt.xlim(0,np.percentile(y,99))


# Add legend and display plotfig = plt.figure(figsize=(8,5)) 

plt.legend()
plt.title(u'Data distribution charateristics) \n' )
plt.xlabel(u'Resistance')
plt.ylabel('Frequency )')
plt.show()

# Store distribution paraemters in a dataframe (this could also be saved)
dist_parameters = pd.DataFrame()
dist_parameters['Distribution'] = (
        results['Distribution'].iloc[0:number_distributions_to_plot])
dist_parameters['Distribution parameters'] = parameters

# Print parameter results
print ('\nDistribution parameters:')
print ('------------------------')

for index, row in dist_parameters.iterrows():
    print ('\nDistribution:', row[0])
    print ('Parameters:', row[1] )

Answer 1

如果您查看以下分类频率分析，您会发现只有 15 个不同的值分布在整个范围内，并且它们之间的差距很大，而不是一个连续的值。一半的观测值的值为 0.211，另外约 36% 的值出现在 1.117 处，约 8% 的值为 0.194，约 4% 的值为 0.001。我认为将其视为连续数据是错误的。