Poisson distribution in python
import numpy as np from scipy.stats import poisson import matplotlib.pyplot as plt import seaborn as sns Example 1 generate Poisson-Distributed Random Variables Numpy
lambda_value = 5 # mean number of occurrences (λ) size = 10 # number of samples to generate poisson_samples = np.random.poisson(lam=lambda_value, size=size) print(poisson_samples) 
Example 2 generate Poisson-Distributed Random Variables Scipy
poisson_samples_2 = poisson.rvs(mu=lambda_value, size=size, random_state=11) print(poisson_samples_2) 
poisson_samples_2.mean() 
poisson_samples_2.std() 
Example 3 Calculating Poisson Probability Mass Function (PMF) Part 1
# is a function that gives the probability that a discrete random variable is exactly
#equal to a particular value. In other words, the PMF describes the distribution of a
#discrete random variable by mapping each possible outcome to its corresponding probability
lambda_value = 5 # mean number of occurrences (λ) k = 3 # number of events # Calculate the probability of exactly k events given an average per year probability = poisson.pmf(k, lambda_value) print(probability) 
#Example 4 Calculating Poisson Probability Mass Function (PMF) Part 2 #lam and mu are the same #array of values
probability2 = poisson.pmf(poisson_samples, mu=lambda_value) print(probability2) 
Example 5 Calculating Cumulative Distribution Function (CDF) - single point
lambda_value = 5 # mean number of occurrences (λ) k = 3 # number of events cumulative_probability = poisson.cdf(k, lambda_value) print(cumulative_probability) 
Example 6 Calculating Cumulative Distribution Function (CDF) - multiple
cumulative_probability2 = poisson.cdf(poisson_samples, lambda_value) print(cumulative_probability2) 
Example 7 Plotting a Poisson Distribution
lambda_value = 5 # mean number of occurrences (λ) k_values = np.arange(0, 15) # range of k values pmf_values = poisson.pmf(k_values, lambda_value) plt.stem(k_values, pmf_values) plt.title(f"Poisson Distribution (λ = {lambda_value})") plt.xlabel('Number of Events (k)') plt.ylabel('Probability') plt.show() 
Example 8 Histogram
lambda_value = 5 # mean number of occurrences (λ)
sample_size = 1000 # number of samples to generate
data = np.random.poisson(lambda_value, sample_size)
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# Create the histogram of counts
plt.hist(data, bins=np.arange(0, 16) – 0.5, edgecolor=’black’, alpha=0.7)
plt.title(f”Poisson Distribution (λ = {lambda_value}, Sample Size = {sample_size})”)
plt.xlabel(‘Number of Events (k)’)
plt.ylabel(‘Count’)
plt.xticks(np.arange(0, 15))
plt.show()
