# Numpy Random Chisquare Distribution

The purpose of this article is to discuss Numpy Random Chisquare distribution and how to utilize the numpy library to produce random numbers and analyze various statistical properties.

## What is Chisquare Distribution?

The chisquare distribution is a continuous probability distribution used in statistics to model the sum of the squares of k independent standard normal random variables.

The chisquare distribution has a single parameter, k, which represents the degrees of freedom.

The PDF of the chisquare distribution is given by:

`f(x; k) = 1/(2^(k/2) * Γ(k/2)) * x^(k/2 - 1) * e^(-x/2)`

where Γ is the gamma function, x is the random variable, and k is the degrees of freedom.

The mean and variance of the chisquare distribution are both equal to k.

## Numpy Random Chisquare

The numpy random chisquare function is used to generate random numbers from a chisquare distribution.

The function takes the degrees of freedom (df) as input and returns an array of random numbers from the chisquare distribution with the specified degrees of freedom.

### Syntax

`numpy.random.chisquare(df, size=None)`

There are Three parameters in it:

 Parameters Overview df (level of freedom). size Displays the array’s shape. None Default value is None, which returns a single random number.

Calculate the chi squared distribution with the following degree of freedom (30) and dimension four by one:

#### Example:

from numpy import random mrx = random.chisquare(df=30, size=(4, 1)) print(mrx)

Make a sample for chi squared probability with degree of freedom 360 and size two by two:

#### Example:

from numpy import random mrx = random.chisquare(df=360, size=(2, 2)) print(mrx)

## ChiSquare Distribution Visualization

The matplotlib library is a popular Python library for data visualization. It provides a wide range of methods to create high-quality plots, including histograms, line plots, scatter plots, and more.

In this case, we can use matplotlib to plot a histogram of the random numbers generated by numpy random chisquare.

Visual representation of the Chi Square Distribution:

#### Example:

from numpy import random import matplotlib.pyplot as pt import seaborn as sbn sbn.distplot(random.chisquare(df=30, size=100), hist=False) pt.show()

Show the Chi Square Distribution with histogram and kernel density estimation:

#### Example:

from numpy import random import matplotlib.pyplot as pt import seaborn as sbn sbn.distplot(random.chisquare(df=360, size=60), hist=True) pt.show()

Numpy random chisquare is useful in many applications.

Some of them shown in below table:

 Applications Overview Statistical Analysis The chisquare distribution is used in statistical analysis to test the goodness of fit of a given model. Numpy random chisquare can be used to generate random data for simulations to test statistical models. Physics The chisquare distribution is used in physics to model the distribution of the sum of squares of errors in measurements. Numpy random chisquare can be used to generate random errors for simulations. Finance The chisquare distribution is used in finance to model the distribution of asset returns. Numpy random chisquare can be used to generate random returns for simulations.

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