Rayleighverdeling

Rayleighverdeling is a continuous probability distribution that describes phenomena where the magnitude of a quantity is related to the square root of the sum of squares of two independent random variables, each with a normal distribution with a mean of zero and equal variance. It is commonly used in signal processing, acoustics, and telecommunications to model the envelope of a randomly sampled narrowband noise signal.

The probability density function (PDF) of the Rayleigh distribution is given by f(x; σ) = (x/σ²) exp(-x²/2σ²), for x ≥ 0, where σ is the scale parameter. This parameter is related to the root mean square of the underlying normal distributions. The cumulative distribution function (CDF) is F(x; σ) = 1 - exp(-x²/2σ²).

The Rayleigh distribution is characterized by its non-negative support and a shape that rises sharply from zero and then decays exponentially. It has a mean of σ√(π/2) and a variance of (2 - π/2)σ². A key property is that it is a special case of the Weibull distribution and is closely related to the Rayleigh fading model, which describes the effects of multipath propagation on radio signals.