5.4 Efron (1975) gives very general definitions of curvature, which generalize (10.1) and

(10.2). For the s-dimensional family (5.1) with covariance matrix θ , if θ is a scalar, define the statistical curvature to be γθ = 

|Mθ |/m3 111/2 where Mθ =

m11 m12 m21 m22 

=

η˙

θ˙ θηθ η˙

θθη¨θ

η¨

θθη˙θ η¨

θθη¨θ



, with η(θ) = {ηi(θ)}, η˙(θ) = {η

i(θ)} and η¨(θ) = {η

i (θ)}. Calculate the curvature of the family (see Example 6.19) C exp

−
n i=1(xi − θ)

m!

for m =2, 3, 4. Are the values of

γθ ordered in the way you expected them to be?