= Log-transformed location-scale model
{title2=$\log T=\alpha+\sigma W$}
If $W$ has <probability density function> $f(w;q)$ and <cumulative distribution function> $F_W(w;q)$, then $T=\exp(\alpha+\sigma W)$, $\sigma>0$, has density $f((\log t-\alpha)/\sigma;q)/(\sigma t)$ and distribution function $F_W((\log t-\alpha)/\sigma;q)$ for $t>0$. The factor $1/(\sigma t)$ follows from the <change-of-variables formula for a probability density>. Upper truncation at $M$ divides the density by $F_W((\log M-\alpha)/\sigma;q)$.
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