STAT330 Lecture Notes - Scale Parameter, Location Parameter

• School: University of Waterloo
• Department: Statistics
• Course: STAT330
• Professor: Christine Dupont

Document Summary

Stat 330 problems - solutions/answers (a) (1 )2. 1. (perform a change of variable, x = tan(u): k , f (x) = 1 tx xtx + xtx+1, e(x) = and v ar(x) = 2t (1 t)2: e(x) and v ar(x) do not exist. (b, k = 1: f (x) = (c, k = 2: f (x) = (cid:16) x (cid:17) 0 (cid:123)(cid:122) (cid:90) c term (2) c (cid:123)(cid:122) term (1) (cid:90) u (cid:90) c (cid:90) c (cid:124) +c: e(x) = and v ar(x) = 2. 1 parameter since f1(x) = f (x; = 1) = Is not a location parameter ( > 0), but is a scale (cid:2)1 + x2(cid:3) 1 and f (x; ) = Is not a scale parameter (you can show this yourself), but is a location parameter since f0(x) = f (x; = 0) = e |x| and f (x; ) = f0 (x ).