What's the equivalent of fitdist and histfit in Python?

Question

--- SAMPLE ---

I have a data set (sample) that contains 1 000 damage values (the values are very small <1e-6) in a 1-dimension array (see the attached .json file). The sample is seemed to follow Lognormal distribution:

--- PROBLEM & WHAT I ALREADY TRIED ---

I tried the suggestions in this post Fitting empirical distribution to theoretical ones with Scipy (Python)? and this post Scipy: lognormal fitting to fit my data by lognormal distribution. None of these works. :(

I always get something very large in Y-axis as the following:

Here is the code that I used in Python (and the data.json file can be downloaded from here):

from matplotlib import pyplot as plt
from scipy import stats as scistats
import json
with open("data.json", "r") as f:
  sample = json.load(f) # load data: a 1000 * 1 array with many small values( < 1e-6)
fig, axis = plt.subplots() # initiate a figure
N, nbins, patches = axis.hist(sample, bins = 40) # plot sample by histogram
axis.ticklabel_format(style = 'sci', scilimits = (-3, 4), axis = 'x') # make X-axis to use scitific numbers
axis.set_xlabel("Value")
axis.set_ylabel("Count")    
plt.show()

fig, axis = plt.subplots()
param = scistats.lognorm.fit(sample) # fit data by Lognormal distribution
pdf_fitted = scistats.lognorm.pdf(nbins, * param[: -2], loc = param[-2], scale = param[-1]) # prepare data for ploting fitted distribution
axis.plot(nbins, pdf_fitted) # draw fitted distribution on the same figure
plt.show()

I tried the other kind of distribution, but when I try to plot the result, the Y-axis is always too large and I can't plot with my histogram. Where did I fail ???

I'have also tried out the suggestion in my another question: Use scipy lognormal distribution to fit data with small values, then show in matplotlib. But the value of variable pdf_fitted is always too big.

--- EXPECTING RESULT ---

Basically, what I want is like this:

And here is the Matlab code that I used in the above screenshot:

fname = 'data.json';
sample = jsondecode(fileread(fname));

% fitting distribution
pd = fitdist(sample, 'lognormal')

% A combined command for plotting histogram and distribution
figure();
histfit(sample,40,"lognormal")

So if you have any idea of the equivalent command of fitdist and histfit in Python/Scipy/Numpy/Matplotlib, please post it !

Thanks a lot !

Answer 1

Try the distfit (or fitdist) library.

https://erdogant.github.io/distfit

pip install distfit

import numpy as np

# Example data
X = np.random.normal(10, 3, 2000)
y = [3,4,5,6,10,11,12,18,20]

# From the distfit library import the class distfit
from distfit import distfit

# Initialize
dist = distfit()

# Search for best theoretical fit on your emperical data
dist.fit_transform(X)

# Plot
dist.plot()

# summay plot
dist.plot_summary()

So in your case it would be:

dist = distfit(distr='lognorm')
dist.fit_transform(X)

Answer 2

Try seaborn:

import seaborn as sns, numpy as np
sns.set(); np.random.seed(0)
x = np.random.randn(100)
ax = sns.distplot(x)

Answer 3

I tried your dataset using Openturns library

x is the list given in you json file.

import openturns as ot
from openturns.viewer import View
import matplotlib.pyplot as plt

# first format your list x as a sample of dimension 1
sample = ot.Sample(x,1) 

# use the LogNormalFactory to build a Lognormal distribution according to your sample
distribution = ot.LogNormalFactory().build(sample)

# draw the pdf of the obtained distribution
graph = distribution.drawPDF()
graph.setLegends(["LogNormal"])
View(graph)
plt.show()

If you want the parameters of the distribution

print(distribution)
>>> LogNormal(muLog = -16.5263, sigmaLog = 0.636928, gamma = 3.01106e-08)

You can build the histogram the same way by calling HistogramFactory, then you can add one graph to another:

graph2 = ot.HistogramFactory().build(sample).drawPDF()
graph2.setColors(['blue'])
graph2.setLegends(["Histogram"])
graph2.add(graph)
View(graph2)

and set the boundaries values if you want to zoom

axes = view.getAxes()
_ = axes[0].set_xlim(-0.6e-07, 2.8e-07)
plt.show()