# Unbounded density?

Dear all,

when I specify a prior with an exponential distribution (as special case of the gamma distribution), mean and standard deviation should be equal to 1/lambda. However, e.g. when I set lambda = 10 (and thus mean and st. dev equal to 0.1), Dynare tells me that the prior distribution for that parameter has unbounded density (even though the exponential distribution has no vertical asymptote). This is, however, not the case for lambda <= 1.
Is this a bug, or am I getting something wrong here?

This is a problem of numerical precision on computers. Given the mean and standard deviation, Dynare needs to solve for the corresponding a and b, i.e. location and shape parameter. The result for a on my machine is `1-1.110223024625157e-16`, which is slightly smaller than 1. Thus, the warning as there is an asymptote for a<1. However, for all practical purposes, it’s equal to 1. Given the limits of floating point arithmetic, there is nothing one can do about it.