Statistics - Rayleigh Distribution

Statistics – Rayleigh Distribution

The Rayleigh distribution is a distribution of steady chance density operate. It’s named after the English Lord Rayleigh. This distribution is broadly used for the next:

  • Communications – to mannequin a number of paths of densely scattered indicators whereas reaching a receiver.
  • Bodily Sciences – to mannequin wind pace, wave heights, sound or mild radiation.
  • Engineering – to examine the lifetime of an object relying upon its age.
  • Medical Imaging – to mannequin noise variance in magnetic resonance imaging.

Rayleigh Distribution

The chance density operate Rayleigh distribution is outlined as:

Formulation

f(x;σ)=xσ2ex22σ2,x0f(x;σ)=xσ2e−x22σ2,x≥0

The place −

  • σσ = scale parameter of the distribution.

The comulative distribution operate Rayleigh distribution is outlined as:

Formulation

F(x;σ)=1ex22σ2,x[0F(x;σ)=1−e−x22σ2,x∈[0∞

Where −

  • σσ = scale parameter of the distribution.

Variance and Expected Value

The expected value or the mean of a Rayleigh distribution is given by:

E[x]=σπ2−−√E[x]=σπ2

The variance of a Rayleigh distribution is given by:

Var[x]=σ24π2