def _cdf(self, x):
logits = self._logits_parameter_no_checks()
total_count = tf.convert_to_tensor(self.total_count)
safe_x = tf.where(x >= 0, x, 0.)
answer = tfp_math.betainc(
total_count, 1. + safe_x, tf.sigmoid(-logits))
return distribution_util.extend_cdf_outside_support(x, answer, low=0)
def _cdf(self, x):
concentration1 = tf.convert_to_tensor(self.concentration1)
concentration0 = tf.convert_to_tensor(self.concentration0)
safe_x = tf.where(tf.logical_and(x >= 0, x < 1), x, 0.5)
answer = tfp_math.betainc(concentration1, concentration0, safe_x)
return distribution_util.extend_cdf_outside_support(
x, answer, low=0., high=1.)
def _cdf(self, x):
logits = self._logits_parameter_no_checks()
total_count = tf.convert_to_tensor(self.total_count)
shape = self._batch_shape_tensor(logits=logits,
total_count=total_count)
safe_x = tf.where(x >= 0, x, 0.)
answer = tf.math.betainc(tf.broadcast_to(total_count, shape),
tf.broadcast_to(1. + safe_x, shape),
tf.broadcast_to(tf.sigmoid(-logits), shape))
return distribution_util.extend_cdf_outside_support(x, answer, low=0)
def _cdf(self, x):
concentration1 = tf.convert_to_tensor(self.concentration1)
concentration0 = tf.convert_to_tensor(self.concentration0)
shape = functools.reduce(
ps.broadcast_shape,
[ps.shape(concentration1),
ps.shape(concentration0),
ps.shape(x)])
concentration1 = tf.broadcast_to(concentration1, shape)
concentration0 = tf.broadcast_to(concentration0, shape)
x = tf.broadcast_to(x, shape)
safe_x = tf.where(tf.logical_and(x >= 0, x < 1), x, 0.5)
answer = tf.math.betainc(concentration1, concentration0, safe_x)
return distribution_util.extend_cdf_outside_support(
x, answer, low=0., high=1.)
def _bdtr(k, n, p):
"""The binomial cumulative distribution function.
Args:
k: floating point `Tensor`.
n: floating point `Tensor`.
p: floating point `Tensor`.
Returns:
`sum_{j=0}^k p^j (1 - p)^(n - j)`.
"""
# Trick for getting safe backprop/gradients into n, k when
# betainc(a = 0, ..) = nan
# Write:
# where(unsafe, safe_output, betainc(where(unsafe, safe_input, input)))
ones = tf.ones_like(n - k)
safe_dn = tf.where(tf.logical_or(k < 0, k >= n), ones, n - k)
dk = tfp_math.betainc(a=safe_dn, b=k + 1, x=1 - p)
return distribution_util.extend_cdf_outside_support(k, dk, low=0, high=n)
def _cdf(self, x):
# Note that igamma returns the regularized incomplete gamma function,
# which is what we want for the CDF.
cdf = tf.math.igamma(self.concentration, self._rate_parameter() * x)
return distribution_util.extend_cdf_outside_support(x, cdf, low=0.)
def _cdf(self, value):
cdf = -tf.math.expm1(-self.rate * value)
# Set cdf = 0 when value is less than 0.
return distribution_util.extend_cdf_outside_support(value, cdf, low=0.)
