I am trying to apply the change of variable theorem for the calculation of the distribution, via the conditional density, of this transformation of joint iid $X_i$ that are N(0,1) variables with no success:
$$f_{X_{(2)}-X_{(1)},...,X_{(n)}-X_{(1)}|X_{(1)}}(x_2,...,x_n)$$
where $X_{(1)}$ is the minimum, $X_{(2)}$ is the second lowest variable and so on (ordered statistic).
Any suggestion?
Thank you.