Geometric Distribution
X ~ Geometric(p)
Memoryless / Waiting-Time Family • Published July 19, 2026
The discrete analogue of the Exponential: history from the Pascal-Fermat correspondence through de Moivre, the only discrete distribution with the memoryless property, a constant discrete hazard function, maximum-likelihood estimation of the success probability (biased in finite samples), and inverse-transform simulation.
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About This Reference Sheet
The discrete analogue of the Exponential: history from the Pascal-Fermat correspondence through de Moivre, the only discrete distribution with the memoryless property, a constant discrete hazard function, maximum-likelihood estimation of the success probability (biased in finite samples), and inverse-transform simulation.
Support
x ∈ {1, 2, 3, ...}
Parameters
p ∈ (0, 1] (success probability)