# Table 1 Proof that $$\varvec{\varTheta }_{\mathcal {EW}}$$ is identifiable

Cases

Hypothesis: $$\varvec{\theta }_{i} \ne \varvec{\theta }_{j}$$

Implication for the thesis

1

$$b_{i} \ne b_{j}$$, $$c_{i}=c_{j}$$ and $$\beta _{i}=\beta _{j}$$

$$F_{EW}\left( t; \varvec{\theta }_{i}\right) \ne F_{EW}\left( t; \varvec{\theta }_{j}\right)$$

2

$$b_{i}=b_{j}$$, $$c_{i}=c_{j}=c$$ and $$\beta _{i} \ne \beta _{j}$$

$$\beta _{i} \ne \beta _{j} \Rightarrow \left( c t\right) ^{\beta _{i}} \ne \left( c t\right) ^{\beta _{j}}$$

3

$$b_{i}=b_{j}$$, $$c_{i} \ne c_{j}$$ and $$\beta _{i}=\beta _{j}=\beta$$

$$c_{i} \ne c_{j} \Rightarrow \left( c_{i} t\right) ^{\beta } \ne \left( c_{j} t\right) ^{\beta }$$

4

$$b_{i}=b_{j}$$, $$c_{i} \ne c_{j}$$ and $$\beta _{i} \ne \beta _{j}$$

$$c_{i} \ne c_{j} \Rightarrow \left( c_{i} t\right) ^{\beta _{i}} \ne \left( c_{j} t\right) ^{\beta _{j}}$$

5

$$b_{i} \ne b_{j}$$, $$c_{i} \ne c_{j}$$ and $$\beta _{i}=\beta _{j}=\beta$$

$$c_{i} \ne c_{j} \Rightarrow \left( c_{i} t\right) ^{\beta } \ne \left( c_{j} t\right) ^{\beta }$$

6

$$b_{i} \ne b_{j}$$, $$c_{i}=c_{j}=c$$ and $$\beta _{i} \ne \beta _{j}$$

$$c_{i}= c_{j} \Rightarrow \left( c t\right) ^{\beta _{i}} \ne \left( c t\right) ^{\beta _{j}}$$

7

$$b_{i} \ne b_{j}$$, $$c_{i} \ne c_{j}$$ and $$\beta _{i} \ne \beta _{j}$$

$$c_{i} \ne c_{j} \Rightarrow \left( c_{i} t\right) ^{\beta _{i}} \ne \left( c_{j} t\right) ^{\beta _{j}}$$