Day 1 · Interactive

Discrete distribution explorer

Drag the sliders and watch the probability mass function change. The goal is to feel how each distribution's story (its parameters) controls its shape, mean, and variance.

Show the plotted values as a table

Things to try

  1. Binomial → symmetric vs skewed. Set p = 0.5 and watch the PMF become symmetric; push p toward 0 or 1 and it skews.
  2. Poisson mean = variance. Change λ and note the mean and variance readouts stay equal. This is the Poisson's defining constraint — and why it so often fails on real ecological counts.
  3. Overdispersion. Switch to Negative Binomial, tick "overlay a Poisson with the same mean," and drag the dispersion k down. The NegBin spreads far wider than the Poisson at the same mean — that extra spread is what clumped ecological data need.
  4. NegBin → Poisson limit. Drag k up to its maximum; the Negative Binomial collapses onto the Poisson.

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