You can use the \(\text{CauchyPDF}\) function to calculate the probability density function (PDF) of the Cauchy-Lorentz distribution.

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

The following variants of this function are available:

  • \(\text{real } \text{CauchyPDF} \left ( \text{<x>}, \text{<location>}, \text{<}\gamma\text{>} \right )\)

Where \(x\), \(location\), and \(\gamma\) are scalar values representing the value of interest, the location or offset (\(x _ 0\)), and the scale term respectively. Note that this function is defined over the range \(\gamma > 0\) 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:

\[\text{CauchyPDF} \left ( x, x _ 0, \gamma \right ) = \frac{1} {\pi \gamma \left [ 1 + \left ( \frac{ x - x _ 0 }{\gamma} \right ) ^ 2 \right ] }\]

Figure 113 shows the basic use of the \(\text{CauchyPDF}\) function.


Figure 113 Example Use Of the CauchyPDF Function