Quick guess:
real<lower=0> mu_sum;
real<lower=1.0 / 3.0, upper=1> mu1_frac;
real<lower=0.5, upper=1> mu2_frac;
mu[1] = mu_sum * mu1_frac;
mu[2] = mu_sum * (1 - mu1_frac) * mu2_frac;
mu[3] = mu_sum * (1 - mu1_frac) * (1 - mu2_frac);
Should span the whole space while ensuring ordering (mu[1] > mu[2] > mu[3]
). But please double check if it works out…
There’s also this: Order the simplex