This hyperprior generates lognormal MTDi distributions with their
coefficients of variation being drawn from a Rayleigh distribution
with mode parameter set to
$$\sigma := CV.$$
Because the standard deviation of this distribution is
$$sd = \sigma \sqrt{(2 - \pi/2)} \approx 0.655 \sigma,$$
this conveniently links our uncertainty about CV to its mode,
and indeed to other measures of centrality that are proportional to this:
$$mean = \sigma \sqrt{\pi/2} \approx 1.25 \sigma$$
$$median = \sigma \sqrt{2 log(2)} \approx 1.18 \sigma.$$
The medians of the lognormal distributions generated are themselves
drawn from a lognormal distribution with meanlog = log(median_mtd)
and sdlog = median_sdlog. Thus, parameter median_sdlog
represents a proportional uncertainty in median_mtd.
CVCoefficient of variation
median_mtdMedian MTDi
median_sdlogProportional uncertainty in median MTDi