Introduction to Python Normal Distribution
Python Normal Distribution
The normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric and bell-shaped.
It is one of the most commonly encountered distributions in statistics and probability theory.
In a normal distribution, the data cluster around the mean value, with fewer observations towards the tails of the distribution.
The probability density function (PDF) of a normal distribution is given by the following formula:
f(x) = (1 / (σ * sqrt(2π))) * exp(-((x - μ)^2) / (2σ^2))
Where:
- μ (mu) represents the mean of the distribution.
- σ (sigma) represents the standard deviation of the distribution.
- π (pi) is a mathematical constant (approximately 3.14159).
- exp() is the exponential function.
- sqrt() is the square root function.
In Python, you can generate random numbers that follow a normal distribution using the numpy.random.normal()
function from the NumPy library.
As an example:
import numpy as np
# Generate random numbers from a normal distribution
mu = 0 # Mean
sigma = 1 # Standard deviation
size = 1000 # Number of random numbers to generate
random_numbers = np.random.normal(mu, sigma, size)
In this example:
- The
np.random.normal(mu, sigma, size)
generates an array of 1000 random numbers from a normal distribution with a mean of 0 and a standard deviation of 1. - You can adjust the values of
mu
andsigma
to control the mean and standard deviation of the distribution, respectively. - The resulting array
random_numbers
will contain the generated random numbers.