Rayleigh Distribution
X ~ Rayleigh(σ)
Magnitude / Signal-Processing Family • Published July 22, 2026
The two-dimensional magnitude analogue of the already-published Half-Normal, and the standard model for received-signal amplitude in wireless propagation: PDF/CDF verified against scipy.stats.rayleigh, exact ties confirmed numerically to the already-published Weibull (k=2 special case) and Chi-Square/Exponential sheets, and -- like the Half-Normal -- a rare fully closed-form maximum-likelihood estimator.
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About This Reference Sheet
The two-dimensional magnitude analogue of the already-published Half-Normal, and the standard model for received-signal amplitude in wireless propagation: PDF/CDF verified against scipy.stats.rayleigh, exact ties confirmed numerically to the already-published Weibull (k=2 special case) and Chi-Square/Exponential sheets, and -- like the Half-Normal -- a rare fully closed-form maximum-likelihood estimator.
Support
x ∈ [0, ∞)
Parameters
σ > 0 (scale)