Poisson distribution implementation in Python

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Poisson distribution is a discrete distribution. It is frequently used to model the counts of event occurrence during a specified time interval, such as telephone calls coming in to a call center in a given day. There is one parameter in the Poisson probability function, λ, which denotes the constant occurring rate in a Poisson process.

X here represents the discrete count numbers, and both mean and variance in a Poisson distribution equal to λt.

To use Poisson distribution with Python, you can simply import module poisson from scipy.stats, and use the corresponding functions:

poisson.pmf() for computation of probability functions,

poisson.cdf() for computation of cumulative probability functions, and

poisson.rvs() for random number generation.

Following code examples show how to use these functions in Python environment.

# How to Calculate Probabilities Using a Poisson Distribution
# You can use the poisson.pmf(k, mu) 
#to calculate probabilities related to the specific count #value from a Poisson distribution.

#Example 1: Probability Equal to Some Value

#A store sells 8 icecreams per day on average. What is the 
#probability that they will sell 10 icecreams on a given day? 

from scipy.stats import poisson

#calculate probability
poisson.pmf(k=10, mu=8)
Out[1]: 0.09926153383153544

#You can use the poisson.cdf(k, mu) functions to calculate 
#cumulative probabilities up to a certain discrete value
# from a given Poisson distribution.

#Example 2: Probability Less than Some Value
#A call center has on average 5 calls coming in per hour. 
# What is the probability that this call center has four or #less incoming calls during a given hour?

from scipy.stats import poisson

#calculate probability
poisson.cdf(k=4, mu=5)
Out[2]: 0.44049328506521257

#Example 3
#generate random values from Poisson distribution with mean=8 #and sample size=20
poisson.rvs(mu=8, size=20)
Out[3]: 
array([ 5, 13,  7,  9, 11, 10,  8,  8,  6,  9,  5,  6,  6, 13,  5,  6,  4, 4, 10, 11], dtype=int64)


#Example 4: Probability where occurence Greater than Some #Value

#A certain shoå sells 25 bottles of PersiMax per day on #average. What is the probability that this shop sells more #than 90 bottles of PersiMax in 3 days?

from scipy.stats import poisson

#calculate probability
1-poisson.cdf(k=90, mu=25*3)
Out[5]: 0.039923967285473094

You can also watch video on our YouTube channel which sheds light on using Python for statistical problem.