I’m trying to fit a lognormal model (code below). This works just fine if I have a vector y. E.g. in R,

```
y <- exp(rnorm(1000))
stan.data <- list(y = y, n = length(y), alpha = 1, beta = 1)
stan.fit <- sampling(stanmodels::lognormal, data = stan.data)
```

where stanmodels::lognormal is defined as:

```
data {
real<lower=0> alpha;
real<lower=0> beta;
int<lower=0> n;
real<lower=0> y[n];
}
parameters {
real mu;
real<lower=0> sigmasq;
}
transformed parameters {
real<lower=0> sigma;
sigma = sqrt(sigmasq);
}
model {
sigmasq ~ inv_gamma(alpha, beta);
mu ~ normal(0, 1000);
y ~ lognormal(mu, sigma);
}
```

However, in my actual problem, I don’t have y. Instead I have mean(y), sd(y), and length(y). Is it possible to still use Stan to achieve the same fit as if I had y? I’m a novice to Stan, and I’ve looked through many examples and the official documentation, but can’t seem to find anything that mentions this problem.

Thanks in advance!

–sundar