This hyperprior generates lognormal MTDi distributions with their coefficients of variation being drawn from a Rayleigh distribution with mode parameter set to

*σ := CV.*

Because the standard deviation of this distribution is

*
sd = σ √(2 - π/2) ~ 0.655 σ,*

this conveniently links our uncertainty about `CV`

to its *mode*,
and indeed to other measures of centrality that are proportional to this:

*
mean = σ √(π/2) ~ 1.25 σ*

*
median = σ √(2 log(2)) ~ 1.18 σ.*

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`

.

`CV`

Coefficient of variation

`median_mtd`

Median MTDi

`median_sdlog`

Proportional uncertainty in median MTDi

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