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)
sdlog = median_sdlog. Thus, parameter
represents a proportional uncertainty in
Coefficient of variation
Proportional uncertainty in median MTDi
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