# 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

dnLoguniform(RealPos min, RealPos max)

### Arguments

 min : RealPos (pass by const reference) The lower bound. max : RealPos (pass by const reference) The upper bound.

### 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)