How can I calculate the cumulative normal distribution in Python?
I am looking for a function in NumPy, SciPy, or any other rigorous Python library that provides the cumulative normal distribution function. Specifically, I want to know how to calculate it using norm.cdf Python.
With my experience in statistical programming, using scipy.stats.norm.cdf is a straightforward way to get the cumulative normal distribution in Python. Here’s how to use it.
from scipy.stats import norm
# Example: Mean = 0, Standard Deviation = 1 (Standard Normal Distribution)
x = 1.5
result = norm.cdf(x)
print(f"Cumulative probability for x={x}: {result}")
This calculates the cumulative probability for the standard normal distribution (mean = 0, standard deviation = 1). Simple and elegant, isn’t it?
Building on Jacqueline’s answer, you can also handle cases with custom mean and standard deviation values. I’ve worked extensively with these distributions, and this is my preferred approach for tailoring normal distribution calculations.
from scipy.stats import norm
# Parameters for the normal distribution
mean = 10
std_dev = 2
x = 12
# Calculate cumulative probability
result = norm.cdf(x, loc=mean, scale=std_dev)
print(f"Cumulative probability for x={x} with mean={mean} and std_dev={std_dev}: {result}")
This flexibility lets you model specific real-world scenarios. For example, in a quality control scenario where you’re comparing a measurement to a process mean, this can be really handy!
Both the previous answers show how to use SciPy’s norm.cdf python directly, but sometimes you might want to integrate NumPy’s capabilities. While NumPy itself doesn’t offer a direct cdf function, you can leverage its strengths for broader data manipulation and combine it with SciPy for the actual computation.
import numpy as np
from scipy.stats import norm
# Use NumPy to generate data and SciPy to compute cdf
x = np.array([0, 1, 2, 3])
result = norm.cdf(x)
print(f"Cumulative probabilities: {result}")
This approach is particularly useful if you have arrays of values and need efficient calculations. Plus, you can extend this by applying NumPy operations on the result to analyze probabilities further.