Probability Distributions with Julia

Weibull Distribution - Worked Example

Julia Workshop

Worked Example

This code performs the following steps:

  1. Imports the Distributions package: This package provides functions for working with various probability distributions in Julia.
using Distributions
  1. Defines the Weibull distribution parameters: The shape and scale parameters are specified.
# Define the Weibull distribution parameters
shape = 2.0
scale = 3.0
  1. Creates a Weibull distribution object: The Weibull function from the Distributions package is used to create a distribution object with the specified parameters.
# Create a Weibull distribution object
dist = Weibull(shape, scale)
  1. Generates random samples: The rand function is used to generate a vector of random samples from the distribution.
# Generate random samples from the distribution
samples = rand(dist, 1000)
# Calculate the probability density function (PDF) at specific points
x_values = [1.0, 2.0, 3.0]
pdf_values = pdf.(dist, x_values)
  1. Calculates PDF, CDF, and quantile values: The pdf, cdf, and quantile functions are used to calculate the probability density, cumulative distribution, and quantile values at specific points.
# Calculate the cumulative distribution function (CDF) at specific points
cdf_values = cdf.(dist, x_values)
# Calculate the quantile function (inverse CDF) at specific probabilities
probabilities = [0.25, 0.5, 0.75]
quantile_values = quantile.(dist, probabilities)
  1. Calculates mean and standard deviation: The mean and std functions are used to calculate the mean and standard deviation of the distribution.
# Calculate the mean and standard deviation of the distribution
mean_dist = mean(dist)
std_dist = std(dist)
  1. Prints the results: The calculated values are printed to the console.
# Print the results
println("Probability density function (PDF) at x = ", x_values, ": ", pdf_values)
println("Cumulative distribution function (CDF) at x = ", x_values, ": ", cdf_values)
println("Quantile function (inverse CDF) at probabilities = ", probabilities, ": ", quantile_values)
println("Mean of the distribution: ", mean_dist)
println("Standard deviation of the distribution: ", std_dist)

This example demonstrates the basic usage of the Weibull distribution in Julia. You can modify the parameters and perform other calculations as needed.