I wouldn't say that it has no classical analog (you spell it your way, I'll spell it my way).
Entanglement occurs whenever the state of a composite system consisting of two spatially separated subsystems fails to factor into a product of states for each subsystem. In classical probability, if you view the "state" as a probability distribution, you can certainly have the situation where the joint probability distribution for two subsystems fails to be factorable into a product of subsystem probability distributions.
Quantum-mechanically, if |\Psi\rangle is the state of the composite system, then the state is factorable if it can be written as:
|\Psi\rangle = |\psi\rangle \otimes |\phi\rangle where |\psi\rangle is the state of the first subsystem, and |\phi\rangle is the state of the second subsystem. If the state cannot be written this way, then the two subsystems are "entangled".
In classical probability theory, if you have one system whose complete state is described by a parameter \alpha, and another system whose complete state is described by a parameter \beta, then the probability distribution P(\alpha, \beta) for the composite system is factorable if it can be written in the form: P(\alpha, \beta) = F(\alpha) \times G(\beta). When that is not the case, people don't use the word "entangled", but it seems analogous.