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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.
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