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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