Location-Scale Family

Definition

Let $X_i={\theta }_1+{\theta }_2{W}_i$, where $W_1,W_2,\dots ,W_n$, be Random Sample from a pdf $f_W(w)$ If $f_{X_i}(x)\stackrel{D}{=}\frac{1}{{\theta }_2}{f}_W\left(\frac{x-{\theta }_1}{{\theta }_2}\right)$, then ${\theta }_1$ is called location parameter and ${\theta }_2$ is called scale parameter