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Fitting a Probability Distribution to data using SciPy's Fit Function

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by sneha@openweaver.com dot icon Updated: Mar 29, 2023

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Fitting a probability distribution to data is identifying a probability distribution that best describes the underlying probability of a given dataset. This is done by finding the distribution parameters (such as the mean, variance, etc.) that best describes the dataset. The parameters are usually estimated using maximum likelihood estimation, which maximizes the likelihood of the data given the estimated parameters. Once the distribution parameters are determined, the distribution can be used to make predictions about future data or make decisions about the data. 



SciPy is a library of open source software for scientific computing in Python. It comprises tools and libraries for numerical computation, analysis, and visualization. It includes modules for linear algebra, integration, optimization, signal processing, and statistics. It can be used for various tasks, from basic statistical processing to advanced numerical simulations. 



The SciPy fit function is a numerical optimization technique used to fit a function to a given set of data points. 

  • It is a part of the SciPy library in Python, which is used for numerical computing. 
  • It uses techniques such as least squares, least absolute deviation, and Nelder-Mead to find an optimal fit for the given data. 


Here is an example of fitting a probability distribution to data using SciPy's fit function 



Fig 1: Preview of the output that you will get on running this code from your IDE

Code


In this solution, we use the SciPy fit function.

Fitting a Custom Scipy Distribution

PythondotLines of Code : 30dotLicense : Strong Copyleft (CC BY-SA 4.0)

Dependent Libraries : 
import numpy as np
from scipy.stats import rv_continuous
from scipy.special import erf
from scipy.special import erfinv

SQRT2 = np.float64(1.4142135623730951)

class lognorm_v2(rv_continuous):

    def _pdf(self, x, μ, σ):
        return 1 / (x * σ * SQRT2 * np.sqrt(np.pi)) * np.exp(-0.5 * ((np.log(x) - μ)/σ)**2)

    def _cdf(self, x, μ, σ):
        return 0.5 + 0.5 * erf((np.log(x) - μ)/ (SQRT2*σ))

    def _ppf(self, x, μ, σ):
        return np.exp(μ + σ * SQRT2 * erfinv(2.0*x - 1.0))

    def _argcheck(self, μ, σ):
        s = σ > 0.0
        return s

np.random.seed(seed=111)
logn = lognorm_v2(name='lognorm_v2', a=0.0, b=np.inf)
test = logn.rvs(μ=2.0,σ=1.0,loc=0.0,scale=1.0, size=100000)

logn.fit(test,floc=0,fscale=1)

(1.9990788106319746, 1.0021523463000124, 0, 1)

Instructions


  1. Install Jupyter Notebook on your computer.
  2. Open terminal and install the required libraries with following commands.
  3. Install SciPy - pip install scipy
  4. Install Numpy - pip install numpy
  5. Copy the snippet using the 'copy' button and paste it into that file.
  6. Run the file using run button.


I hope you found this useful. I have added the link to dependent libraries, version information in the following sections.


I found this code snippet by searching for "Fitting a probability distribution to data using SciPy's fit function" in kandi. You can try any such use case!

Dependent Libraries

scipyby scipy

Python doticonstar image 11340 doticonVersion:v1.11.0rc1doticon
License: Permissive (BSD-3-Clause)

SciPy library main repository

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            scipyby scipy

            Python doticon star image 11340 doticonVersion:v1.11.0rc1doticon License: Permissive (BSD-3-Clause)

            SciPy library main repository
            Support
              Quality
                Security
                  License
                    Reuse

                      numpyby numpy

                      Python doticonstar image 23755 doticonVersion:v1.25.0rc1doticon
                      License: Permissive (BSD-3-Clause)

                      The fundamental package for scientific computing with Python.

                      Support
                        Quality
                          Security
                            License
                              Reuse

                                numpyby numpy

                                Python doticon star image 23755 doticonVersion:v1.25.0rc1doticon License: Permissive (BSD-3-Clause)

                                The fundamental package for scientific computing with Python.
                                Support
                                  Quality
                                    Security
                                      License
                                        Reuse

                                          If you do not have SciPy or numpy that is required to run this code, you can install it by clicking on the above link and copying the pip Install command from the numpy page in kandi.


                                          You can search for any dependent library on kandi like numpy/SciPy.

                                          Environment Tested


                                          I tested this solution in the following versions. Be mindful of changes when working with other versions.

                                          1. The solution is created in Python3.9.6
                                          2. The solution is tested on SciPy-Python 1.9.1 version.


                                          Using this solution, we are able to fit a probability distribution to data using SciPy's fit function.

                                          This process also facilities an easy to use, hassle free method to create a hands-on working version of code which would help us to fit a probability distribution to data.

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