Python Scipy Stats Fit + Examples

The “Python Scipy Stats Fit” is a concept that will be covered in this Python tutorial. It teaches us how to fit given or generated data to various distributions, including gamma, normal, and others. Include the subsequent topics as well.

  • Python Scipy Stats Fit Distribution
  • Python Scipy Stats Fit Normal Distribution
  • Python Scipy Stats Fit Gamma Distribution
  • Python Scipy Stats Fit Exponential Distribution
  • Python Scipy Stats Fit Beta
  • Python Scipy Stats Fit Pareto
  • Python Scipy Stats Fit Chi2

Python Scipy Stats Fit Distribution

The method of choosing the statistical distribution that best fits a collection of data is known as distribution fitting. The normal, Weibull, Gamma, and Smallest Extreme Value distributions are a few examples of statistical distributions.

A distribution that fairly represents our data is essential. If we use the incorrect distribution, the results of our computations in comparison to the requirements won’t be a true reflection of what the process generates.

In order to find the distribution that best matches the data, several distributions are often evaluated against the data. We cannot simply glance at the distribution’s shape and conclude that it fits our data well.

How do we decide which distribution is best? The various distributions’ parameters are estimated using statistical approaches. These factors establish the distribution. Location, scale, shape, and threshold are the four parameters that are used in distribution fitting. For each distribution, not all parameters exist. Estimating the parameters that determine the various distributions is the process of fitting a distribution.

The distribution’s location parameter indicates where it is located on the x-axis (the horizontal axis). How much dispersion there is in the distribution is determined by the scale parameter. The distribution can adopt a variety of shapes according to the shape parameter. The distribution’s minimal value along the x-axis is determined by the threshold parameter.

Here in this tutorial, we will estimate the parameters for the distributions using the Python Scipy methods.

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Read: Python Scipy Load Mat File

Python Scipy Stats Fit Normal Distribution

For independent, random variables, the normal distribution, sometimes referred to as the Gaussian distribution, is the most significant probability distribution in statistics. Most individuals are aware of its well-known bell-shaped curve from statistical reports.

The majority of the observations are centered around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean. The probabilities for values that are farther from the mean taper off equally in both directions. Extreme values in the distribution’s two tails are likewise rare.

As we talked about the four parameters for the distribution, Estimates for the shape parameters are not always returned by distributions. Normal distribution, for instance, just provides position and scale estimates.

Here in this section, we will fit the data to a normal distribution by following the below steps:

Import the required libraries or methods using the below python code.

from scipy import stats

Generate some data that fits using the normal distribution, and create random variables.

a,b=1.,1.1
x_data = stats.norm.rvs(a, b, size=700, random_state=120)

Now fit for the two parameters using the below code.

loc_param, scale_param = stats.norm.fit(x_data)
print(loc_param)
print(scale_param)
Python Scipy Stats Fit Normal Distribution
Python Scipy Stats Fit Normal Distribution

From the output, the best parameter values for normal distribution are 1.04(loc) and 1.11(scale). This is how to fit the data to normal distribution.

Read: Python Scipy Stats Kurtosis

Python Scipy Stats Fit Gamma Distribution

The continuous probability distribution known as the gamma distribution is frequently used in many scientific disciplines to model continuous variables with skewed distributions that are always positive. It happens spontaneously in processes where the intervals between occurrences are significant.

This distribution comes in two different forms. Shape, scale, and threshold are the three parameters that make up the three-parameter gamma distribution. It is a two-parameter gamma distribution when the threshold parameter value is set to 0.

Let’s fit the data to Gamma Distribution by following the below steps:

Import the required libraries or methods using the below python code.

from scipy import stats

Generate some data that fits using the gamma distribution, and create random variables.

a = 1.
x_data = stats.gamma.rvs(a,size=1000, random_state=120)

Now fit for the three parameters using the below code.

shape_param, scale_param, thres_param = stats.gamma.fit(x_data)
print(shape_param)
print(scale_param)
print(thres_param)
Python Scipy Stats Fit Gamma Distribution
Python Scipy Stats Fit Gamma Distribution

From the output, the best parameter values for gamma distribution are 1.07(shape), 0.001(scale), and 0.95(threshold). This is how to fit the data to a gamma distribution.

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Read: Python Scipy Stats Multivariate_Normal

Python Scipy Stats Fit Exponential Distribution

Continuous probability distribution with a right skew called the exponential distribution represents variables where tiny values occur more frequently than larger values. Probability is continually decreasing as data values rise, with small values having comparatively high probabilities.

The exponential distribution comes in two different forms. Naturally, the two-parameter variant has two parameters: scale and threshold. The distribution changes to a one-parameter exponential distribution when the threshold parameter is set to zero. Here in this section, we will fit data to Exponential Distribution.

Import the required libraries or methods using the below python code.

from scipy import stats

Generate some data that fits using the exponential distribution, and create random variables.

x_data = stats.expon.rvs(size=1000, random_state=120)

Now fit for the two parameters using the below code.

scale_param, thres_param = stats.expon.fit(x_data)
print(scale_param)
print(thres_param)
Python Scipy Stats Fit Exponential Distribution
Python Scipy Stats Fit Exponential Distribution

From the output, the best parameter values for exponential distribution are 0.0013(scale) and 1.033(threshold). This is how to fit the data to an exponential distribution.

Read: Python Scipy Freqz 

Python Scipy Stats Fit Beta

A continuous probability distribution called the beta distribution is used to model random variables whose values fall within a given range. Use it to model subject regions with a range of possible values that includes both an upper and bottom bound.

The beta distribution has two shape parameters, and, in contrast to other distributions with shape and scale parameters. Positive values for both parameters are required. Here in this section, we will fit data to Beta Distribution.

Import the required libraries or methods using the below python code.

from scipy import stats

Generate some data that fits using the beta distribution, and create random variables.

a,b =1.0,1.3
x_data = stats.beta.rvs(a,b,size=800, random_state=115)

Now fit for the parameters using the below code.

stats.beta.fit(x_data)
Python Scipy Stats Fit Beta
Python Scipy Stats Fit Beta

From the output, we can see the best parameters for the beta distribution.

Read: Python Scipy Confidence Interval

Python Scipy Stats Fit Pareto

The Pareto distribution is skewed and has long tails that are “slowly fading.” A shape parameter (also known as a slope parameter or the Pareto Index) and a location parameter together constitute the Pareto distribution, which was proposed by the Italian economist Vilfredo Pareto in the 19th century.

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Here in this section, we will fit data to Pareto Distribution by following the below steps:

Import the required libraries or methods using the below python code.

from scipy import stats

Generate some data that fits using the pareto distribution, and create random variables.

b =1.3
x_data = stats.pareto.rvs(b,size=1000, random_state=100)

Now fit for the three parameters using the below code.

shape_param, loc_param, scale_param = stats.pareto.fit(x_data)
print(shape_param)
print(loc_param)
print(scale_param)
Python Scipy Stats Fit Pareto
Python Scipy Stats Fit Pareto

From the output, we have concluded that the best parameter values for pareto distribution are 1.28(shape), -0.0(loc), and 1.005(scale). This is how to fit the data to a pareto distribution.

Read: Python Scipy Chi-Square Test 

Python Scipy Stats Fit Chi2

A family of continuous probability distributions is known as the chi-square (X2) distributions. They are frequently used in hypothesis tests, such as the chi-square test of independence and the goodness of fit test.

The parameter k, which stands for the degrees of freedom, determines the shape of a chi-square distribution.

Import the required libraries or methods using the below python code.

from scipy import stats

Generate some data that fits using the chi2 distribution, and create random variables.

k = 40
x_data = stats.chi2.rvs(k,size=800, random_state=115)

Now fit for the three parameters using the below code.

shape_param, loc_param, scale_param = stats.chi2.fit(x_data)
print(shape_param)
print(loc_param)
print(scale_param)
Python Scipy Stats Fit Chi2
Python Scipy Stats Fit Chi2

From the output, the best parameter values for chi2 distribution are 34.12(shape), 3.68(loc), and 1.05(scale). This is how to fit the data to a chi2 distribution.

Also, take a look at some more Python SciPy tutorials.

So, in this tutorial, we have learned about the “Python Scipy Stats Fit” and covered the following topics.

  • Python Scipy Stats Fit Distribution
  • Python Scipy Stats Fit Normal Distribution
  • Python Scipy Stats Fit Gamma Distribution
  • Python Scipy Stats Fit Exponential Distribution
  • Python Scipy Stats Fit Beta
  • Python Scipy Stats Fit Pareto
  • Python Scipy Stats Fit Chi2