# Python Probability Distributions – Normal, Binomial, Poisson, Bernoulli

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## 1. Python Probability Distributions – Objective

After studying Python Descriptive Statistics, now we are going to explore 4 Major Python Probability Distributions: Normal, Binomial, Poisson, and Bernoulli Distributions in Python. Moreover, we will learn how to implement these Python probability distributions with Python Programming.

## 2. What is Python Probability Distribution?

A probability distribution is a function under probability theory and statistics- one that gives us how probable different outcomes are in an experiment. It describes events in terms of their probabilities; this is out of all possible outcomes. Let’s take the probability distribution of a fair coin toss. Here, heads take a value of X=0.5 and tails gets X=0.5 too.
Two classes of such a distribution are discrete and continuous. The former represented by a probability mass function and the latter by a probability density function.
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## 3. How to Implement Python Probability Distributions?

Let’s implement these types of Python Probability Distributions, let’s see them:

### a. Normal Distribution in Python

Python normal distribution is a function that distributes random variables in a graph that is shaped as a symmetrical bell. It does so by arranging the probability distribution for each value. Let’s use Python numpy for this.

```>>> import scipy.stats
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> np.random.seed(1234)
>>> samples=np.random.lognormal(mean=1.,sigma=.4,size=10000)
>>> shape,loc,scale=scipy.stats.lognorm.fit(samples,floc=0)
>>> num_bins=50
>>> clr="#EFEFEF"
>>> counts,edges,patches=plt.hist(samples,bins=num_bins,color=clr)
>>> centers=0.5*(edges[:-1]+edges[1:])
>>> cdf=scipy.stats.lognorm.cdf(edges,shape,loc=loc,scale=scale)
>>> prob=np.diff(cdf)
>>> plt.plot(centers,samples.size*prob,'k-',linewidth=2)```

[<matplotlib.lines.Line2D object at 0x0359E890>]

`>>> plt.show()` Implement Python Probability Distributions – Normal Distribution in Python

### b. Binomial Distribution in Python

Python binomial distribution tells us the probability of how often there will be a success in n independent experiments. Such experiments are yes-no questions. One example may be tossing a coin.
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```>>> import seaborn
>>> from scipy.stats import binom
>>> data=binom.rvs(n=17,p=0.7,loc=0,size=1010)
>>> ax=seaborn.distplot(data,
kde=True,
color='pink',
hist_kws={"linewidth": 22,'alpha':0.77})
>>> ax.set(xlabel='Binomial',ylabel='Frequency')```

[Text(0,0.5,’Frequency’), Text(0.5,0,’Binomial’)]

`>>> plt.show()` Implement Python Probability Distributions – Binomial Distribution in Python

### c. Poisson Distribution in Python

Python Poisson distribution tells us about how probable it is that a certain number of events happen in a fixed interval of time or space. This assumes that these events happen at a constant rate and also independent of the last event.

```>>> import numpy as np
>>> s=np.random.poisson(5, 10000)
>>> import matplotlib.pyplot as plt
>>> plt.hist(s,16,normed=True,color='Green')```

(array([5.86666667e-03, 3.55200000e-02, 8.86400000e-02, 1.48906667e-01,
1.91573333e-01, 1.81440000e-01, 1.56160000e-01, 1.16586667e-01,
6.65600000e-02, 3.90400000e-02, 2.06933333e-02, 9.06666667e-03,
3.84000000e-03, 2.13333333e-03, 5.33333333e-04, 1.06666667e-04]), array([ 0. , 0.9375, 1.875 , 2.8125, 3.75 , 4.6875, 5.625 ,
6.5625, 7.5 , 8.4375, 9.375 , 10.3125, 11.25 , 12.1875,
13.125 , 14.0625, 15. ]), <a list of 16 Patch objects>)
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`>>> plt.show()` Implement Python Probability Distributions – Poisson Distribution in Python

### d. Bernoulli Distribution in Python

Python  Bernoulli Distribution is a case of binomial distribution where we conduct a single experiment. This is a discrete probability distribution with probability p for value 1 and probability q=1-p for value 0. p can be for success, yes, true, or one. Similarly, q=1-p can be for failure, no, false, or zero.

```>>> s=np.random.binomial(10,0.5,1000)
>>> plt.hist(s,16,normed=True,color='Brown')```

(array([0.00177778, 0.02311111, 0. , 0.08711111, 0. ,
0.18666667, 0. , 0.33777778, 0.45155556, 0. ,
0.37688889, 0. , 0.224 , 0. , 0.07466667,
0.01422222]), array([0. , 0.5625, 1.125 , 1.6875, 2.25 , 2.8125, 3.375 , 3.9375,
4.5 , 5.0625, 5.625 , 6.1875, 6.75 , 7.3125, 7.875 , 8.4375,
9. ]), <a list of 16 Patch objects>)
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`>>> plt.show()` Implement Python Probability Distributions – Bernoulli Distribution in Python

So, this was all about Python Probability Distribution. Hope you like our explanation.

## 4. Conclusion

Hence, we studied Python Probability Distribution and its 4 types with an example. In addition, we learned how to implement these Python probability distributions. Furthermore, if you have any doubt, feel free to ask in the comment section.
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