Hi everyone,

I’m trying to estimate a single parameter of the three-parameter Weibull distribution with its two other parameters fixed (known). The fit seems to be ok and the diagnostics do not show any weird behavior. However, the effective number of parameters estimated by the loo package is larger than one (1.7). How is this possible? I thought that it should be between 0 and 1. I obtain even larger effective number of parameters for more data points (below a small subset is given). Probably I am missing something obvious or misunderstand something. Thank you in advance for your help.

The loo results:

```
Computed from 4000 by 10 log-likelihood matrix
Estimate SE
elpd_loo -63.0 7.8
p_loo 1.7 0.8
looic 126.1 15.6
Pareto k diagnostic values:
Count Pct
(-Inf, 0.5] (good) 9 90.0%
(0.5, 0.7] (ok) 1 10.0%
(0.7, 1] (bad) 0 0.0%
(1, Inf) (very bad) 0 0.0%
All Pareto k estimates are ok (k < 0.7)
```

The R code:

```
Kmin = 20
lambda = 4
Kmat = c(119.90595, 28.73428, 81.63255, 76.59204, 79.39576, 130.57210, 141.26851, 107.11765, 32.11837, 29.06687)
N = length(Kmat)
data = list(N = N,
Kmat = Kmat,
Kmin = Kmin,
lambda = lambda)
stan_mod = 'built_in_weib.stan'
# stan_mod = 'custom_weib.stan'
fit = stan(file = stan_mod, data = data,
iter = 2000, chains = 4)
log_lik_m = extract_log_lik(fit)
loo_m = loo(log_lik_m)
print(loo_m)
```

stan code (built_in_weib.stan):

```
data {
int<lower=1> N; // # observations
real Kmin;
real lambda;
vector[N] Kmat; // observations
}
parameters {
real<lower=Kmin> Km;
}
model {
target += weibull_lpdf(Kmat-Kmin | lambda, Km-Kmin);
}
generated quantities {
vector[N] log_lik;
for (n in 1:N) {
log_lik[n] = weibull_lpdf(Kmat[n]-Kmin | lambda, Km-Kmin);
}
}
```