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Gamma

Positive sums and waiting time to multiple arrivals; contains exponential and chi-square.
Type continuousSupport x > 0Family Waiting time
Probability densityf(x) = xᵅ⁻¹e⁻ˣ⁄ᶿ / (Γ(α)θᵅ)
continuous

Gamma in motion

0.02.95.88.712
Supportx > 0
Mean3
Variance3
Connections

Where the gamma
comes from — and leads.

Every link is one of the four moves from the relationship map: special cases, transformations, limits, and Bayesian conjugacy.

Chi-square← α=k/2, θ=2

Chi-square(k) is Gamma(k/2, 2).

Special caseExponentialα = 1

Gamma with shape one is exponential.

Special caseChi-squareα=k/2, θ=2

The chi-square family lies on a gamma parameter slice.

Special case

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See every connection at once.

The relationship map draws the whole backbone — special cases, transformations, limits, and conjugacies — in one guided view.

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