= Shifted lognormal distribution
{title2=$\log(X-\theta)\sim N(m,\sigma^2)$}
The support is $x>\theta$ and the <probability density function> is
$$
f(x)=\frac{\exp[-(\log(x-\theta)-m)^2/(2\sigma^2)]}{(x-\theta)\sigma\sqrt{2\pi}}.
$$
The <change of variables> $z=\log(x-\theta)$ proves normalization. The threshold $\theta$ is a lower endpoint, distinct from the log-mean $m$ and log-standard-deviation $\sigma$. In measured <sea-ice pressure ridge> spacings, finite ridge widths and detection rules can create such a lower endpoint.
Back to article page
