Other Common Random Distributions in Python

📊 Other Common Random Distributions in Python

After Normal (Gaussian) distribution, NumPy can generate other statistical distributions like Uniform, Binomial, Poisson, and Exponential. Let’s go through each with examples and visualization.

1️⃣ Uniform Distribution

Generates numbers evenly distributed between low and high.

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns# Generate uniform data
data = np.random.uniform(low=0, high=10, size=1000)# Histogram
sns.histplot(data, bins=30, kde=True, color='skyblue')
plt.title("Uniform Distribution")
plt.xlabel("Value")
plt.ylabel("Frequency")
plt.show()

import numpy as np

import matplotlib.pyplot as plt

import seaborn as sns# Generate uniform data

data = np.random.uniform(low=0, high=10, size=1000)# Histogram

sns.histplot(data, bins=30, kde=True, color='skyblue')

plt.title("Uniform Distribution")

plt.xlabel("Value")

plt.ylabel("Frequency")

plt.show()

Values are equally likely between 0 and 10
kde=True shows the smooth density curve

2️⃣ Binomial Distribution

Simulates success/failure experiments, e.g., coin flips.

# Parameters
n = 10 # number of trials
p = 0.5 # probability of success
size = 1000# Generate binomial data
data = np.random.binomial(n, p, size)# Visualization
sns.histplot(data, bins=10, kde=False, color='orange')
plt.title("Binomial Distribution (n=10, p=0.5)")
plt.xlabel("Number of Successes")
plt.ylabel("Frequency")
plt.show()

# Parameters

n = 10 # number of trials

p = 0.5 # probability of success

size = 1000# Generate binomial data

data = np.random.binomial(n, p, size)# Visualization

sns.histplot(data, bins=10, kde=False, color='orange')

plt.title("Binomial Distribution (n=10, p=0.5)")

plt.xlabel("Number of Successes")

plt.ylabel("Frequency")

plt.show()

Peaks around n*p (expected value)
Discrete distribution

3️⃣ Poisson Distribution

Models count of events in a fixed interval.

Values are integers (0,1,2…)
Mean ≈ λ

4️⃣ Exponential Distribution

Models time between events, continuous.

Values ≥ 0
Skewed distribution, decays exponentially

5️⃣ Multinomial Distribution

Used for categorical outcomes with probabilities.

Output (example):

Each row = number of outcomes per trial
Each column = category

🧠 Summary Table of Distributions

Distribution	Function	Key Parameters	Type
Normal	`np.random.normal()`	loc, scale, size	Continuous
Uniform	`np.random.uniform()`	low, high, size	Continuous
Binomial	`np.random.binomial()`	n, p, size	Discrete
Poisson	`np.random.poisson()`	lam, size	Discrete
Exponential	`np.random.exponential()`	scale, size	Continuous
Multinomial	`np.random.multinomial()`	n, pvals, size	Discrete

🎯 Practice Exercises

Generate 5000 numbers from uniform distribution (0–100) and plot histogram.
Simulate 100 coin flips with probability 0.3 and plot frequency of heads.
Generate Poisson data with λ=7 and visualize it.
Generate exponential data with scale=3 and plot histogram + KDE.

Other Common Random Distributions in Python