You can use the \(\text{RayleighPDF}\) function to calculate the probability density function (PDF) of the of the Rayleigh distribution.

You can use the \rayleighp backslash command to insert this function.

The following variants of this function are available:

  • \(\text{real } \text{RayleighPDF} \left ( \text{<x>}, \text{<}\sigma\text{>} \right )\)

Where \(x\) and \(\sigma\) are scalar values representing the value of interest and the scale term respectively. Note that this function is defined over the range \(\sigma > 0\) and will generate a runtime error or return NaN for values for which the function is not defined.

The value is calculated directly using the relation:

\[\text{RayleighPDF} \left ( x, \sigma \right ) = \frac{x}{\sigma ^ 2} e ^ {- \frac{x ^ 2}{2 \sigma ^ 2} }\]

Figure 190 shows the basic use of the \(\text{RayleighPDF}\) function.


Figure 190 Example Use Of the RayleighPDF Function