I am very new to probabilistic modeling in general and was trying to run the Pareto/NBD model from this post (https://github.com/datascienceinc/oreilly-intro-to-predictive-clv/blob/master/oreilly-an-intro-to-predictive-clv-tutorial.ipynb) but have been running into initialization issues for my data set. Any help is greatly appreciated.

This is the error I am running into and the model is below.

```
Rejecting initial value:
Log probability evaluates to log(0), i.e. negative infinity.
Stan can't start sampling from this initial value.
Rejecting initial value:
Log probability evaluates to log(0), i.e. negative infinity.
Stan can't start sampling from this initial value.
Initialization between (-1, 1) failed after 100 attempts.
Try specifying initial values, reducing ranges of constrained values, or reparameterizing the model.
```

```
data{
int<lower=0> n_cust; //number of customers
vector<lower=0>[n_cust] x;
vector<lower=0>[n_cust] tx;
vector<lower=0>[n_cust] T;
}
parameters{
// vectors of lambda and mu for each customer.
// Here I apply limits between 0 and 1 for each
// parameter. A value of lambda or mu > 1.0 is unphysical
// since you don't enough time resolution to go less than
// 1 time unit.
vector <lower=0,upper=1.0>[n_cust] lambda;
vector <lower=0,upper=1.0>[n_cust] mu;
// parameters of the prior distributions : r, alpha, s, beta.
// for both lambda and mu
real <lower=0>r;
real <lower=0>alpha;
real <lower=0>s;
real <lower=0>beta;
}
model{
// temporary variables :
vector[n_cust] like1; // likelihood
vector[n_cust] like2; // likelihood
// Establishing hyperpriors on parameters r, alpha, s, and beta.
r ~ normal(0.5,0.1);
alpha ~ normal(10,1);
s ~ normal(0.5,0.1);
beta ~ normal(10,1);
// Establishing the Prior Distributions for lambda and mu :
lambda ~ gamma(r,alpha);
mu ~ gamma(s,beta);
// The likelihood of the Pareto/NBD model :
like1 = x .* log(lambda) + log(mu) - log(mu+lambda) - tx .* (mu+lambda);
like2 = (x + 1) .* log(lambda) - log(mu+lambda) - T .* (lambda+mu);
// Here we increment the log probability density (target) accordingly
target+= log(exp(like1)+exp(like2));
}
```