Figure 4

The credibility distribution of \(\pmb{\xi\sim\mathcal{N}(a, b)}\) in Example 4 . The piecewise function \(\Phi(x)\) is the credibility distribution of \(\xi\sim\mathcal{N}(a, b)\) whose values are \(\frac{1}{2} e^{-1}\), 0.5, and \(1-\frac{1}{2} e^{-1}\) when x are \(a-b\), a, and \(a+b\), respectively. In addition, \(\Phi(x)\) approaches 0 as \(x\rightarrow-\infty\) and approaches 1 as \(x\rightarrow+\infty\).