# Python – Non-Central Chi-squared Distribution in Statistics

• Last Updated : 10 Jan, 2020

scipy.stats.ncx2() is a non-central chi-squared continuous random variable. It is inherited from the of generic methods as an instance of the rv_continuous class. It completes the methods with details specific for this particular distribution.

Parameters :

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q : lower and upper tail probability
x : quantiles
loc : [optional]location parameter. Default = 0
scale : [optional]scale parameter. Default = 1
size : [tuple of ints, optional] shape or random variates.
moments : [optional] composed of letters [‘mvsk’]; ‘m’ = mean, ‘v’ = variance, ‘s’ = Fisher’s skew and ‘k’ = Fisher’s kurtosis. (default = ‘mv’).

Results : non-central chi-squared continuous random variable

Code #1 : Creating non-central chi-squared continuous random variable

 `# importing library`` ` `from` `scipy.stats ``import` `ncx2  ``   ` `numargs ``=` `ncx2.numargs ``a, b ``=` `4.32``, ``3.18``rv ``=` `ncx2(a, b) ``   ` `print` `(``"RV : \n"``, rv)  `

Output :

```RV :
scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D6E0FE08
```

Code #2 : non-central chi-squared continuous variates and probability distribution

 `import` `numpy as np ``quantile ``=` `np.arange (``0.01``, ``1``, ``0.1``) `` ` `# Random Variates ``R ``=` `ncx2.rvs(a, b) ``print` `(``"Random Variates : \n"``, R) `` ` `# PDF ``R ``=` `ncx2.pdf(a, b, quantile) ``print` `(``"\nProbability Distribution : \n"``, R) `

Output :

```Random Variates :
1.452454339214702

Probability Distribution :
[0.10195838 0.10369453 0.10528707 0.1067405  0.10805931 0.1092479
0.11031066 0.1112519  0.11207589 0.11278684]

```

Code #3 : Graphical Representation.

 `import` `numpy as np ``import` `matplotlib.pyplot as plt ``    ` `distribution ``=` `np.linspace(``0``, np.minimum(rv.dist.b, ``3``)) ``print``(``"Distribution : \n"``, distribution) ``    ` `plot ``=` `plt.plot(distribution, rv.pdf(distribution)) `

Output :

```Distribution :
[0.         0.04081633 0.08163265 0.12244898 0.16326531 0.20408163
0.24489796 0.28571429 0.32653061 0.36734694 0.40816327 0.44897959
0.48979592 0.53061224 0.57142857 0.6122449  0.65306122 0.69387755
0.73469388 0.7755102  0.81632653 0.85714286 0.89795918 0.93877551
0.97959184 1.02040816 1.06122449 1.10204082 1.14285714 1.18367347
1.2244898  1.26530612 1.30612245 1.34693878 1.3877551  1.42857143
1.46938776 1.51020408 1.55102041 1.59183673 1.63265306 1.67346939
1.71428571 1.75510204 1.79591837 1.83673469 1.87755102 1.91836735
1.95918367 2.        ]
``` Code #4 : Varying Positional Arguments

 `import` `matplotlib.pyplot as plt ``import` `numpy as np ``    ` `x ``=` `np.linspace(``0``, ``5``, ``100``) ``    ` `# Varying positional arguments ``y1 ``=` `ncx2 .pdf(x, ``1``, ``3``) ``y2 ``=` `ncx2 .pdf(x, ``1``, ``4``) ``plt.plot(x, y1, ``"*"``, x, y2, ``"r--"``) `

Output : My Personal Notes arrow_drop_up