# $$\text{CauchyPDF}$$¶

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