cdfRayleigh#

Purpose#

Computes the Rayleigh cumulative distribution function.

Format#

p = cdfRayleigh(x, scale)#

Parameters:

x (NxK matrix, Nx1 vector or scalar) – Values at which to evaluate the cumulative distribution function for the Rayleigh distribution. \(x \geq 0\).
scale (NxK matrix, Nx1 vector or scalar) – Scale parameter, ExE conformable with x. \(scale > 0\).

Returns:

p (NxK matrix, Nx1 vector or scalar) – Each element in p is the cumulative distribution function of the Rayleigh distribution evaluated at the corresponding element in x.

Examples#

Here is an example show the Rayleigh cumulative distribution plot with different scale parameters.

// Values
x = seqa(0, 0.1, 100);

// Scale
scale = 0.5~1~2~3~4;

// Call Rayleigh function
p = cdfRayleigh(x, scale);

plotxy(x, p);

After running above code,

Remarks#

The Rayleigh cumulative distribution function is defined as

\[1 − exp⁡(\frac{-x^2}{2\sigma^2})\]