tf.contrib.distributions.QuantizedDistribution.log_cdf()

tf.contrib.distributions.QuantizedDistribution.log_cdf(value, name='log_cdf')

Log cumulative distribution function.

Given random variable X, the cumulative distribution function cdf is:

log_cdf(x) := Log[ P[X <= x] ]

Often, a numerical approximation can be used for log_cdf(x) that yields a more accurate answer than simply taking the logarithm of the cdf when x << -1.

Additional documentation from QuantizedDistribution:

For whole numbers y,

cdf(y) := P[Y <= y]
        = 1, if y >= upper_cutoff,
        = 0, if y < lower_cutoff,
        = P[X <= y], otherwise.

Since Y only has mass at whole numbers, P[Y <= y] = P[Y <= floor(y)]. This dictates that fractional y are first floored to a whole number, and then above definition applies.

The base distribution's log_cdf method must be defined on y - 1.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

• logcdf: a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.