Rev Language Reference
dnLoguniform - Log-Uniform Distribution
A strictly positive real number x has a log-uniform distribution over interval (min,max) if its logarithm y = ln(x) has uniform distribution over interval (ln(min),ln(max)).
Usage
Arguments
| min : | RealPos (pass by const reference) |
| The lower bound. | |
| max : | RealPos (pass by const reference) |
| The upper bound. |
Domain Type
Details
The log-uniform distribution is defined over strictly positive real numbers. Saying that x is log-uniform is equivalent to saying that y = ln(x) is uniform. The log-uniform distribution therefore expresses lack of information about the order of magnitude of a scale parameter: if x has a log-uniform distribution, then it has equal chance to be contained by any of the intervals of the form (10^k, 10^(k+1)) within the allowed range.
The density is p(x) = 1/x, which can be seen by defining x = exp(y) where y has uniform distribution and apply the change-of-variable formula.
The log-uniform distribution is improper when defined over the entire positive real line. To always make it proper, in RevBayes, a min and a max should always be specified.
Example
# a log-uniform prior over the rate of change of a Brownian trait (or a Brownian relaxed clock)
trueTree = readTrees("data/primates.tree")[1]
sigma ~ dnLogUniform(min=0.001, max=1000)
X ~ dnBrownian(trueTree,sigma)
# ...
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