\(\text{LogNormalCDF}\)

You can use the \(\text{LogNormalCDF}\) function to calculate the cumulative distribution function (CDF) of the log-normal distribution.

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

The following variants of this function are available:

  • \(\text{real } \text{LogNormalCDF} \left ( \text{<x>} \right )\)

  • \(\text{real } \text{LogNormalCDF} \left ( \text{<x>}, \text{<}\mu\text{>} \right )\)

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

Where \(x\), \(\mu\), and \(\sigma\) are scalar values representing the value of interest, the mean value and the standard deviation. If not specified, the mean value will be 0 and the standard deviation will be 1. Note that this function is defined over the range \(x > 0\) and \(\sigma > 0\). The \(\text{LogNormalCDF}\) function 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:

\[\text{LogNormalCDF} \left ( x, \mu, \sigma \right ) = \frac{1}{2} + \frac{1}{2} \text{erf} \left [ \frac{ \ln \left ( x \right ) - \mu }{\sqrt{2} \sigma } \right ]\]

Figure 171 shows the basic use of the \(\text{LogNormalCDF}\) function.

../_images/log_normal_cdf_example.png

Figure 171 Example Use Of the LogNormalCDF Function