# scipy stats.gompertz() | Python

scipy.stats.gompertz() is an Gompertz (or truncated Gumbel) 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 : Gompertz (or truncated Gumbel) continuous random variable

Code #1 : Creating Gompertz (or truncated Gumbel) continuous random variable

 `from` `scipy.stats ``import` `gompertz  ` ` `  `numargs ``=` `gompertz.numargs ` `[a] ``=` `[``0.7``, ] ``*` `numargs ` `rv ``=` `gompertz(a) ` ` `  `print` `(``"RV : \n"``, rv)  `

Output :

```RV :
<scipy.stats._distn_infrastructure.rv_frozen object at 0x000001E39A3E2470>
```

Code #2 : Gompertz (or truncated Gumbel) random variates and probability distribution

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

Output :

```Random Variates :
[1.29938059 1.47547887 1.33324567 1.79424061 0.45304378 1.46222247
1.29260365 0.59989705 3.58467676 1.81226267]

Probability Distribution :
[0.01993441 0.19813875 0.34179784 0.45591617 0.54485437 0.61240685
0.66187043 0.69610503 0.71758726 0.72845776]```

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.         0.06122449 0.12244898 0.18367347 0.24489796 0.30612245
0.36734694 0.42857143 0.48979592 0.55102041 0.6122449  0.67346939
0.73469388 0.79591837 0.85714286 0.91836735 0.97959184 1.04081633
1.10204082 1.16326531 1.2244898  1.28571429 1.34693878 1.40816327
1.46938776 1.53061224 1.59183673 1.65306122 1.71428571 1.7755102
1.83673469 1.89795918 1.95918367 2.02040816 2.08163265 2.14285714
2.20408163 2.26530612 2.32653061 2.3877551  2.44897959 2.51020408
2.57142857 2.63265306 2.69387755 2.75510204 2.81632653 2.87755102
2.93877551 3.        ]```

Code #4 : Varying Positional Arguments

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

Output :

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