The function "A"("θ"), or equivalently "g"("θ"), is automatically determined once the other functions have been chosen, since it must assume a form that causes the distribution to be normalized (sum or integrate to one over the entire domain). Furthermore, both of these functions can always be written as functions of "η", even when "η"("θ") is not a one-to-one function, i.e. two or more different values of "θ" map to the same value of "η"("θ"), and hence "η"("θ") cannot be inverted. In such a case, all values of "θ" mapping to the same "η"("θ") will also have the same value for "A"("θ") and "g"("θ").