Why These Distributions Matter
Three Powerful Continuous Models
The Beta, Weibull, and Pareto distributions complete your toolkit for continuous probability. Beta belongs to the core Exam P path. Weibull and Pareto are optional enrichment for broader probability and risk study.
Where You'll See Them
Beta Distribution
Models proportions, percentages, and probabilities themselves. Test pass rates, market shares, batting averages — any quantity constrained to [0, 1].
Weibull Distribution
The workhorse of reliability engineering. Models equipment failure times with flexible failure rates: increasing (wear-out), decreasing (burn-in), or constant (Exponential).
Pareto Distribution
The heavy-tailed distribution behind the “80/20 rule.” Essential for insurance claim modeling, income distributions, and any situation where extreme values dominate.
Connections to What You Know
• Beta(1,1) = Uniform(0,1) — the simplest Beta is the Uniform!
• Weibull(k=1, λ) = Exponential(1/λ) — the Exponential is a special Weibull
• If X ~ Pareto(α, θ), then ln(1 + X/θ) ~ Exponential(α)