I would like to randomly sample a discrete distribution called the Borel distribution. The Borel distribution is similar to the Poisson distribution, and is defined as:

I have calculated the log likelihood and have implemented it. (I cannot, unfortunately, upload the latex for this as I am a new user.)

Using the class definition of the Poisson distribution as reference, I defined the following class:

```
import numpy as np
import theano.tensor as tt
from scipy import stats
import warnings
from pymc3.util import get_variable_name
from pymc3.distributions.dist_math import bound, factln, binomln, betaln, logpow, random_choice
from pymc3.distributions.distribution import Discrete, draw_values, generate_samples
from pymc3.distributions.shape_utils import broadcast_distribution_samples
from pymc3.math import tround, sigmoid, logaddexp, logit, log1pexp
from pymc3.theanof import floatX, intX, take_along_axis
class Borel(Discrete):
def __init__(self, mu, *args, **kwargs):
super().__init__(*args, **kwargs)
self.mu = mu = tt.as_tensor_variable(floatX(mu))
self.mode = intX(tt.floor(p))
def random(self, point=None, size=None):
#SOME foo
return None
def logp(self, value):
mu = self.mu
log_prob = bound(
logpow(mu*value, value-1) - factln(value) - mu*value,
mu >= 0, value >= 0)
# Return zero when mu and value are both zero
return tt.switch(tt.eq(mu, 0) * tt.eq(value, 0),
0, log_prob)
```

How would I calculate the random distribution of the Borel Distribution using PyMC3?