Rayleightyyppinen

Rayleightyyppinen is a Finnish term used in statistics, physics and engineering to describe phenomena, models, or distributions that exhibit Rayleigh-type behavior. The form is derived from Lord Rayleigh, and in Finnish scholarly usage it denotes properties associated with the Rayleigh distribution or with envelopes produced by two-dimensional Gaussian components.

A Rayleigh-distributed variable X with scale parameter σ > 0 has probability density function f(x) = (x/σ^2) exp(-x^2/(2σ^2)) for x ≥ 0, and a cumulative distribution function F(x) = 1 − exp(-x^2/(2σ^2)). Its mean is μ = σ√(π/2) and its variance is Var = (4 − π)/2 · σ^2. In Finnish texts, the label Rayleightyyppinen is used to describe a random quantity or a model that follows this distribution, or to describe the envelope of a two-dimensional Gaussian field.

The Rayleigh form arises as the magnitude of a vector whose components are independent Gaussian variables with zero mean. In practical terms, it models the envelope of complex-valued signals in wireless communications without a line-of-sight component, and the amplitude of scattered light or sound fields.

In engineering, Rayleightyyppinen behavior is used to characterize fading channels (Rayleigh fading), radar and sonar signal processing, and optical coherence contexts where the detected amplitude follows a Rayleigh law. The distribution is related to, but distinct from, the Rice distribution, which adds a dominant component. It is also connected to the exponential distribution via the square of the Rayleigh variable. Related topics include the Rayleigh distribution, Rayleigh fading, and the Rice distribution.