Statistics Toolbox

Rayleigh Distribution

The following sections provide an overview of the Rayleigh distribution.

Background of the Rayleigh Distribution

The Rayleigh distribution is a special case of the Weibull distribution. If A and B are the parameters of the Weibull distribution, then the Rayleigh distribution with parameter is equivalent to the Weibull distribution with parameters and .

If the component velocities of a particle in the x and y directions are two independent normal random variables with zero means and equal variances, then the distance the particle travels per unit time is distributed Rayleigh.

Definition of the Rayleigh Distribution

The Rayleigh pdf is

Parameter Estimation for the Rayleigh Distribution

The raylfit function returns the MLE of the Rayleigh parameter. This estimate is

Example and Plot of the Rayleigh Distribution

The following commands generate a plot of the Rayleigh pdf.

• x = [0:0.01:2];
  p = raylpdf(x,0.5);
  plot(x,p)
  
  
  

Poisson Distribution

Student's t Distribution