Why do you allow the creation of a normal distribution with nan as the mean when validate_args=True?

If you execute the following code

from tensorflow_probability import distributions as tfd

tfd.Normal(loc=0, scale=float("nan"), validate_args=True)

we get the following error

tensorflow.python.framework.errors_impl.InvalidArgumentError: Expected 'tf.Tensor(False, shape=(), dtype=bool)' to be true. Summarized data: b'Argument scale must be positive.'
b'Condition x > 0 did not hold element-wise:'
b'x (shape=() dtype=float32) = 'nan

Maybe this error message could be improved, given that NaN is not greater, smaller or equal to zero (in Python).

float("nan") > 0
False
float("nan") < 0
False
float("nan") == 0
False

Furthermore, the following program does not produce any error

from tensorflow_probability import distributions as tfd

tfd.Normal(loc=float("nan"), scale=1, validate_args=True)

which means that we can create a normal distribution with NaN as the mean, but this should probably not be allowed (especially when validate_args=True, which is the case), or is there any reason why this was done?

Maybe these issues also occur with other distributions. I haven't checked it.

Start by reproducing the two tfd.Normal examples with validate_args=True and compare the validation behavior for loc and scale. Then inspect Normal's argument-validation entry point and related distribution validations to determine the intended NaN handling. Done means the behavior and error reporting are consistent with the agreed validation policy, with regression coverage for the reported cases.