The log-uniform distribution is useful in cases where inputs cover large ranges of values, but little is known about their underlying distribution. In a loguniform distribution, the logtransformed random variable is assumed to be uniformly distributed.

f(x,a,b) =   

1/(x(log(b)-log(a))) for a⇐x⇐b   

0 otherwise

support a ⇐ x ⇐ b