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scipy stats.chi() | Python
• Last Updated : 20 Mar, 2019

scipy.stats.chi() is an chi continuous random variable that is defined with a standard format and some shape parameters to complete its specification.

Parameters :
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 : chi continuous random variable

Special Cases :

• chi(1, loc, scale) = halfnormal
• chi(2, 0, scale) = rayleigh
• chi(3, 0, scale) : maxwell

Code #1 : Creating chi continuous random variable

 `# importing scipy``from` `scipy.stats ``import` `chi `` ` `numargs ``=` `chi.numargs``[a] ``=` `[``0.6``, ] ``*` `numargs``rv ``=` `chi(a)`` ` `print` `(``"RV : \n"``, rv) `

Output :

```RV :
<scipy.stats._distn_infrastructure.rv_frozen object at 0x000002948537C6D8>
```

Code #2 : chi random variates and probability distribution.

 `import` `numpy as np``quantile ``=` `np.arange (``0.01``, ``1``, ``0.1``)``  ` `# Random Variates``R ``=` `chi.rvs(a, scale ``=` `2``,  size ``=` `10``)``print` `(``"Random Variates : \n"``, R)`` ` `# PDF``R ``=` `chi.pdf(a, quantile, loc ``=` `0``, scale ``=` `1``)``print` `(``"\nProbability Distribution : \n"``, R)`

Output :

```Random Variates :
[2.40483665 1.68478304 0.01664071 2.48977805 3.66286843 1.68463842
0.14434643 0.67812242 0.46190886 1.99973997]

Probability Distribution :
[0.01384193 0.14349716 0.25719966 0.35519439 0.43801475 0.50641521
0.56131243 0.60373433 0.63477687 0.65556791]
```

Code #3 : Graphical Representation.

 `import` `numpy as np``import` `matplotlib.pyplot as plt`` ` `distribution ``=` `np.linspace(``0``, np.minimum(rv.dist.b, ``5``))``print``(``"Distribution : \n"``, distribution)`` ` `plot ``=` `plt.plot(distribution, rv.pdf(distribution))`

Output :

```Distribution :
Distribution :
[0.         0.10204082 0.20408163 0.30612245 0.40816327 0.51020408
0.6122449  0.71428571 0.81632653 0.91836735 1.02040816 1.12244898
1.2244898  1.32653061 1.42857143 1.53061224 1.63265306 1.73469388
1.83673469 1.93877551 2.04081633 2.14285714 2.24489796 2.34693878
2.44897959 2.55102041 2.65306122 2.75510204 2.85714286 2.95918367
3.06122449 3.16326531 3.26530612 3.36734694 3.46938776 3.57142857
3.67346939 3.7755102  3.87755102 3.97959184 4.08163265 4.18367347
4.28571429 4.3877551  4.48979592 4.59183673 4.69387755 4.79591837
4.89795918 5.        ]```

Code #4 : Varying Positional Arguments

 `import` `matplotlib.pyplot as plt``import` `numpy as np`` ` `x ``=` `np.linspace(``0``, ``5``, ``100``)`` ` `# Varying positional arguments``y1 ``=` `chi.pdf(x, ``1``, ``6``)``y2 ``=` `chi.pdf(x, ``1``, ``4``)``plt.plot(x, y1, ``"*"``, x, y2, ``"r--"``)`

Output :

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