Editing Log-normal distribution (section)

=== Cumulative distribution function ===
<!-- erf changed into erfc because then the formula is slightly shorter, and besides the expression with erf is already present in the floating box -->
The [[cumulative distribution function]] is

<math display="block"> F_X(x) = \Phi{\left( \frac{\ln x - \mu} \sigma \right)} </math>

where <math> \Phi </math> is the cumulative distribution function of the standard normal distribution (i.e., {{nowrap|<math> \operatorname\mathcal{N}( 0, 1 ) </math>).}}

This may also be expressed as follows:<ref name=":1" />

<math display="block"> \frac{1}{2} \left[ 1 + \operatorname{erf} \left(\frac{\ln x - \mu}{\sigma\sqrt{2}}\right) \right] = \frac12 \operatorname{erfc} \left(-\frac{\ln x - \mu}{\sigma\sqrt{2}}\right) </math>

where {{big|{{math|erfc}}}} is the [[complementary error function]].