The assumptions of the fiducial argument, here explained in terms of the invertibility of the functional model, ensure that the terms indeed add up, and that a well-behaved distribution will surface. We can choose the statistical model in such a way that the sample statistic \(\hat{\theta}(s)\) and the parameter \(\theta\) are related in the right way: relative to the parameter \(\theta\), we have a distribution over the statistic \(\hat{\theta}\), but by the same token we have a distribution over parameters relative to this statistic. As a result, the probability function \(P_{\theta}(R_{\hat{\theta}(s) + \epsilon})\) over \(\epsilon\), where \(\theta\) is fixed, can be transferred to a fiducial probability function \(P_{\theta + \epsilon}(R_{\hat{\theta}(s)})\) over \(\epsilon\), where \(\hat{\theta}(s)\) is fixed. The function \(P_{\theta}(R_{\hat{\theta}})\) of the parameter \(\theta\) is thus a proper probability function, from which a credal interval can be constructed.