# Weibull Distribution with priors on shape and scale diverges

I have a variable that is Weibull Distributed

 Duration ~ dweib(Shape,Scale)


The Shape and Scale parameters are distributed to log-normal and Weibull distributions, respectively.

 Shape ~ dlnorm(Hyperlogmean,HyperlogPrecision)
Scale ~ dweib(Hyperweibshape,Hyperweibullscale)


I am having trouble with the standard deviations for Duration from the model.

Here are the parameter estimates from RJAGS

                      MEAN          SD
Duration            4.154e+55    2.275e+58
Scale               3.809e-01    1.813e+00
Shape               2.696e+00    2.455e+00
Hyperlogmean        6.965e-01    7.889e-02
HyperlogPrecision   1.751e+00    2.562e-01
HyperWeibullScale   7.236e-02    2.259e-02
HyperWeibullShape   3.529e-01    3.223e-02


Here are the corresponding quantiles:

                       2.5%       25%        50%      75%      97.5%
Duration             2.058e-01  1.481557   4.05502 2.729e+01 5.091e+05
Scale                1.758e-06  0.001968   0.02439 0.17805   3.045e+00
Shape                4.420e-01  1.199896   2.00382 3.355e+00 9.083e+00
HyperLogMean         5.413e-01  0.643618   0.69648 7.495e-01 8.515e-01
HyperLogPrecision    1.286e+00  1.571430   1.73832 1.916e+00 2.288e+00
HyperWeibullScale    3.774e-02  0.056396   0.06917 8.478e-02 1.255e-01
HyperWeibullShape    2.924e-01  0.330716   0.35193 3.742e-01 4.184e-01


I am thinking that my problem is coming from the HyperWeibullScale parameter partly because its 97.5% quartile becomes very large when it transformed from RJAGS Weibull parameterization to the R Weibull parameterization. Most of my mixing trace plots and MCMC diagnostics look fine.

I am wondering whether the high standard deviation for Duration has to do with my choice of priors.