Add Gamma, Negative Binomial, and Generalized Poisson Distribution (#145

)

* Add Gamma and Negative binomial distribution

* Implement Generalized Poisson Distribution(GPD)

appletree/randgen.py

@@ -11,6 +11,7 @@
 
 from appletree.utils import exporter
 
+
 export, __all__ = exporter(export_self=False)
 
 if jax.config.x64_enabled:
@@ -85,6 +86,32 @@ def poisson(key, lam, shape=()):
     return key, rvs.astype(INT)
 
 
+@export
+@partial(jit, static_argnums=(3,))
+def gamma(key, alpha, beta, shape=()):
+    """Gamma distribution random sampler.
+
+    Args:
+        key: seed for random generator.
+        alpha: <jnp.array>-like shape in gamma distribution.
+        beta: <jnp.array>-like rate in normal distribution.
+        shape: output shape.
+            If not given, output has shape jnp.broadcast_shapes(jnp.shape(alpha), jnp.shape(beta)).
+
+    Returns:
+        an updated seed, random variables.
+
+    """
+    key, seed = random.split(key)
+
+    shape = shape or jnp.broadcast_shapes(jnp.shape(alpha), jnp.shape(beta))
+    alpha = jnp.broadcast_to(alpha, shape).astype(FLOAT)
+    beta = jnp.broadcast_to(beta, shape).astype(FLOAT)
+
+    rvs = random.gamma(seed, alpha, shape=shape) / beta
+    return key, rvs.astype(FLOAT)
+
+
 @export
 @partial(jit, static_argnums=(3,))
 def normal(key, mean, std, shape=()):
@@ -249,6 +276,78 @@ def _binomial_dispatch(seed, p, n):
     return key, jnp.reshape(ret, shape)
 
 
+@export
+@partial(jit, static_argnums=(3, 4))
+def negative_binomial(key, p, n, shape=()):
+    """Negative binomial distribution random sampler. Using Gamma–Poisson mixture.
+
+    Args:
+        key: seed for random generator.
+        p: <jnp.array>-like probability of a single success in negative binomial distribution.
+        n: <jnp.array>-like number of successes in negative binomial distribution.
+        shape: output shape.
+            If not given, output has shape jnp.broadcast_shapes(jnp.shape(p), jnp.shape(n)).
+
+    Returns:
+        an updated seed, random variables.
+
+    References:
+        1. https://en.wikipedia.org/wiki/Negative_binomial_distribution#Gamma%E2%80%93Poisson_mixture  # noqa
+        2. https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.nbinom.html
+
+    """
+
+    key, lam = gamma(key, n, p / (1 - p), shape)
+
+    key, rvs = poisson(key, lam)
+    return key, rvs
+
+
+@export
+@partial(jit, static_argnums=(3,))
+def generalized_poisson(key, lam, eta, shape=()):
+    """Generalized Poisson Distribution(GPD) random sampler.
+
+    Args:
+        key: seed for random generator.
+        lam: <jnp.array>-like expectation(location parameter) in GPD.
+        eta: <jnp.array>-like scale parameter in GPD, within [0, 1).
+        shape: output shape. If not given, output has shape jnp.shape(lam).
+
+    Returns:
+        an updated seed, random variables.
+
+    References:
+        1. https://gist.github.com/danmackinlay/00e957b11c488539bd3e2a3804922b9d
+        2. https://search.r-project.org/CRAN/refmans/LaplacesDemon/html/dist.Generalized.Poisson.html  # noqa
+
+    """
+
+    shape = shape or jnp.broadcast_shapes(jnp.shape(lam), jnp.shape(eta))
+    lam = jnp.broadcast_to(lam, shape).astype(FLOAT)
+    eta = jnp.broadcast_to(eta, shape).astype(FLOAT)
+
+    key, population = poisson(key, lam * (1 - eta), shape)
+
+    offspring = jnp.copy(population)
+
+    def cond_fun(args):
+        return jnp.any(args[1] > 0)
+
+    def body_fun(args):
+        key, offspring = poisson(args[0], eta * args[1])
+        population = args[2] + offspring
+        return key, offspring, population
+
+    key, offspring, population = jax.lax.while_loop(
+        cond_fun,
+        body_fun,
+        (key, offspring, population),
+    )
+
+    return key, population.astype(INT)
+
+
 @export
 @jit
 def uniform_key_vectorized(key):