PDF line in distribution fitting (Python)

Question

I am trying to fit the data using distribution fitting in python.

Problem: The probability Density Function (PDF) line on histogram is not complete as shown in the image. Is there a way to get the PDF line for all data?. I'm not sure if I am making mistake in setting the correct axis or scale. For instance 'density=True' argument correctly or array bin_centers for my x-axis?

I tried to fix this using existing answer, but I couldnt able to solve the problem.

Test data: Available here

Script I am using:

import pandas as pd
import numpy as np
import scipy
import scipy.stats
import matplotlib.pyplot as plt
from sklearn.preprocessing import StandardScaler
from sklearn import datasets
from numpy import percentile

#%% Test dataset
y=pd.read_csv('Clean.csv',squeeze=True,na_filter=True,header=None,index_col=None) 

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

df=pd.DataFrame(data=y)

fig = plt.figure(figsize=(9, 3))
plt.hist(y)
plt.show()

# Create an index array (x) for data
#%%


y_std=round(y)

import warnings
warnings.filterwarnings("ignore")


dist_names = ['beta',
              'expon',
                'exponnorm',
                'lognorm',
              'pearson3'
               ]

# Set up empty lists to stroe results
chi_square = []
p_values = []
KS = []
# Set up 50 bins for chi-square test
# Observed data will be approximately evenly distrubuted aross all bins
percentile_bins = np.linspace(0,80,31)
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)
    param = dist.fit(y_std)   
    p = scipy.stats.kstest(y_std, distribution, args=param)[1]
    p = np.around(p, 5)
    p_values.append(p) 
    
    
    ks = scipy.stats.kstest(y_std, distribution, args=param)
    ks = np.around(ks, 5)
    KS.append((distribution,ks[0],ks[1]))
    
    
    # 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])
    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}")
        
# 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['KS_Test'] = KS
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 = 20
bin_cutoffs = np.linspace(np.percentile(y,0), np.percentile(y,99),number_of_bins)

# Create the plot
fig = plt.figure(figsize=(7, 5))
h = plt.hist(y, bins = bin_cutoffs, color='0.75')

# 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)
      # Separate parts of parameters
   
    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,90))

# Add legend and display plot

plt.legend()
plt.show()

Answer 1

Creating Pareto plots is also possible with the distfit library. The colors/linewidth etc can easily be customized. More information can be found on the documentation pages. But here is an example:

# Import
from distfit import distfit
import numpy as np

# Create dataset
X = np.random.normal(0, 2, 10000)
# Initialize
dfit = distfit()
# Fit
dfit.fit_transform(X)

# Plot
fig, ax = dfit.plot(chart='PDF', n_top=10)