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.

Slots

CV

Coefficient of variation

median_mtd

Median MTDi

median_sdlog

Proportional uncertainty in median MTDi