Cutpoint inclusivity (Sec 15.5)

[jerome-white]

In the cutpoint equations presented in Section 15.5 (Eq. 15.7, 15.8, 15.9, and 15.10), the intervals for the discrete outcome variable seem exclusive. From Eq. 15.7 for example:

y_i = {
   1 if z_i < 0,
   2 if z_i \in (0, c_2),
   ...,
}

Should the intervals be left-inclusive? So 2 z_i \in [0, c_2) instead?

This appears in both my Kindle (2020 Nov) and my paperback edition (ISBN 978-1-107-67651-0)

[andrewgelman]

Yes, you're literally correct but it doesn't matter because the distribution is continuous so there's probability zero of being right on any boundary.