estimation parameter GB2 in stan

[a.kordba...@gmail.com]

Hello everybody

i have a question for you all , It is my pleasure if you can help me to solve the problem.
my question is :

I want to estimate the parameters of finite mixture model .
please check the attachment.  

but i can not do it very well.

functions {

  real GB2_lpdf(real y, real a, real b, real p, real q) {

    log_gb2 = log(fabs(a)) + log(y) * (a * p - 1)

             - (log(b) * a * p + lbeta(p, q)

                + log(1 + (y / b)^a) * (p + q));

    return log_gb2;

  }

}

data {

  int<lower=0> N;

  int<lower=0> K; // maybe K = 2

  vector[N] Y;

  matrix[3, N] x;

}

parameters {

  vector[K] mu;

  vector[K] alpha;

  vector[K] beta[3];

  vector[K] a;

  vector<lower=0>[K] p;

  vector<loser=0>[K] q;

}

model {

  real log_E;

  for (i in 1:N)  {

    for (k in 1:K) {

      log_E = mu[k] + alpha[k] * F[i] + beta[1, k] * x[1, i]

             + beta[2, k] * x[2, i] + beta[3, k] * x[3, i];

      b[i, k] = exp(log_E + lbeta(p[k], q[k])

                    - lbeta(p[k] + 1 / a[k], q[k] - 1 / a[k]));

      Y[i] ~ GB2(a[k], b[i, k], p[k], q[k]);

    }

  }

  

  // Priors

  mu ~ normal(0, 100);

  alpha ~ normal(0, 100);

  for (j in 1:3)

    beta[j] ~ normal(0, 100);

  a ~ normal(0, 100);

  p ~ gamma(0.001, 0.001);

  q ~ gamma(0.001, 0.001);

}

[Bob Carpenter]

What problem are you having.

First, test your function. You can use generated quantities to
run it on particular values or use RStan to expose the function
and test it through R.

Second, generate fake data and make sure you can fit that.

- Bob

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