Mixture with custom distribution class

Questions
1

I need to create a mixture model with Exponential distribution positioned at different places.
I tried several approaches: using Deterministic distribution, using DensityDist distribution.
But all they failed for some pymc3 issues. Finally I have written a custom distribution.
It does not fail with exception but does not sample.

class ShExponential(pm.Exponential):
    def __init__(self, mu, lam, *args, **kwargs):
        super(ShExponential, self).__init__(lam, *args, **kwargs)
        self.mu = tt.as_tensor_variable(mu)
        self.mean += self.mu
        self.mode += self.mu
        self.median += self.mu

    def logp(self, value):
        return super(ShExponential, self).logp(value - self.mu)

    def random(self, point=None, size=None):
        mu = pm.distributions.draw_values([self.mu], point=point, size=size)[0]
        return super(ShExponential, self).random(point=point, size=size) + mu

def stick_breaking(beta):
    portion_remaining = tt.concatenate([[1], tt.extra_ops.cumprod(1 - beta)[:-1]])
    return beta * portion_remaining

with pm.Model() as model:
    alpha = pm.Gamma('alpha', 1., 1.)
    beta = pm.Beta('beta', 1, alpha, shape=K)
    w = pm.Deterministic('w', stick_breaking(beta))

    lam = pm.Uniform('lam', 1., 2., shape=K)
    exp = pm.Exponential('exp', lam, shape=K)
    mu = pm.Uniform('mu', 1., 100., shape=K)
    obs = pm.Mixture('obs', w, ShExponential.dist(mu, lam), observed=x)
    step = pm.Metropolis()
    trace = pm.sample(1000, step=step, random_seed=SEED)

All samples in “trace” are identical.
What is wrong with my class?

2

I dont think this is a good way to implement it - it would be easier to debug just copy and modify the Exponential logp here