VISUAL LESSON · 1 PICTURES

Continuous Distribution Atlas

Which continuous distribution matches the story behind the data?

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BEFORE THE FIRST PICTURE

How this lesson unfolds.

Begin with Which continuous distribution fits the story? Use the picture, intuition and explanation together before moving on.

Continuous distribution field guide comparing Uniform, Exponential, Normal, Gamma, Beta, Chi-square, Student's t, F, Weibull and Log-normal distributions. — Picture 1 of 1 · tap to inspect in full resolution

Which continuous distribution fits the story?

INTUITION

Uniform models equal chance across a bounded range; exponential one waiting time; normal symmetric aggregation; gamma several waiting events; beta an unknown proportion; chi-square squared variation; Student's t uncertain small-sample means; F variance ratios; Weibull lifetimes; and log-normal multiplicative growth. Shape is a clue—support and assumptions decide.

MATHEMATICAL STATEMENT

Uniform models equal chance across a bounded range; exponential one waiting time; normal symmetric aggregation; gamma several waiting events; beta an unknown proportion; chi-square squared variation; Student's t uncertain small-sample means; F variance ratios; Weibull lifetimes; and log-normal multiplicative growth.

Learning goalDistinguish common continuous distributions by support, shape and generating story.
Helpful foundationscontinuous probability · probability density functions
Common trapA curve's appearance is only a clue; its support, parameters and generating assumptions determine whether the model is appropriate.
Next connectionStudy each distribution's parameters, support, CDF and real-data assumptions.