
EXAMPLES AND APPLICATIONS 171
0 50 100 150
0.0 0.2 0.4 0.6 0.8 1.0
y
~
pl
y
(y
~
)
(a) Plausibility function of
˜
Y
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0
G
Y
(Y
~
)
CDF
(b) Distribution function of G
Y
(
˜
Y )
Figure 9.1 Taken from [179]. Panel (a): Plausibility function of
˜
Y in the log-normal data
example. Panel (b): Distribution function of G
Y
(
˜
Y ) (gray) compared with that of Unif(0, 1)
(black) based on Monte Carlo samples from the log-normal distribution with µ = 2.173 and
σ
2
= 2.3808, the maximum likelihood estimates in the example from [21].
9.3.3 Gamma models
Let Y = (Y
1
,.. . ,Y
n
) be an iid sample from a gamma distribution with shape param-
eter θ
1
> 0 and