Pivotal quantity

[elodie]

I am reading the following in a textbook.

X1,..., Xn is (iid) distributed according to a parametric family with
parameters a and theta. Both a and theta are unknown.
(...an argument I am skipping...)
P( Xmin^theta / a^theta <t ) =1-1/t
therefore
Xmin^theta / a is a pivotal quantity.

I am surprised, I would have said: Xmin^theta / a^theta is a pivotal
quantity.

I would appreciate some help with this small problem. Thanks in
advance.

[Jack Tomsky]

From the cdf that you are quoting from the book, you are right in that (Xmin^theta)/(a^theta) = (Xmin/a)^theta is a pivotal quantity.

Jack