Gamma Distribution
X ~ Gamma(α, β)
Sum-of-Exponentials Family • Published July 19, 2026
The waiting-time-for-the-n-th-event distribution: history from Euler's Gamma function through Erlang's queueing generalization of the Exponential, shape-rate vs. shape-scale parameterization pitfalls, the full property list including the Fisher information matrix, maximum-likelihood estimation via a transcendental digamma equation, and simulation via the Erlang sum-of-Exponentials construction.
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About This Reference Sheet
The waiting-time-for-the-n-th-event distribution: history from Euler's Gamma function through Erlang's queueing generalization of the Exponential, shape-rate vs. shape-scale parameterization pitfalls, the full property list including the Fisher information matrix, maximum-likelihood estimation via a transcendental digamma equation, and simulation via the Erlang sum-of-Exponentials construction.
Support
x ∈ (0, ∞)
Parameters
α > 0 (shape), β > 0 (rate)