Statistics notation: what does a tilde under a letter mean?

Question

Like this:

Now, assume that $T\Bigl(\underset{\sim}X\Bigl)$ is sufficient for $\sigma$ when $\mu$ is fixed.

Then,

$f\bigl(X_1=x_1,X_2=x_2,X_3=x_3,...X_n=x_n\bigl)=g\biggl(T\Bigl(\underset{\sim}x\Bigl)\biggl)h\Bigl(x\Bigl)$

Is it meaning $x_1+x_2+...+x_n$?

Thank you!

Answer 1

It usually means a vector of observations when written by hand. So in this context, it must have been mentioned before that $\underline X=(X_1,X_2,\ldots,X_n)$.