  This article is written for pedagogical purposes aiming at practitioners
trying to estimate the finite support of continuous probability distributions,
i.e., the minimum and the maximum of a distribution defined on a finite domain.
Generalized Pareto distribution GP({\theta}, {\sigma}, {\xi}) is a
three-parameter distribution which plays a key role in Peaks-Over-Threshold
framework for tail estimation in Extreme Value Theory. Estimators for GP often
lack analytical solutions and the best known Bayesian methods for GP involves
numerical methods. Moreover, existing literature focuses on estimating the
scale {\sigma} and the shape {\xi}, lacking discussion of the estimation of the
location {\theta} which is the lower support of (minimum value possible in) a
GP. To fill the gap, we analyze four two-parameter subclasses of GP whose
conjugate priors can be obtained analytically, although some of the results are
known. Namely, we prove the conjugacy for {\xi} > 0 (Pareto), {\xi} = 0
(Shifted Exponential), {\xi} < 0 (Power), and {\xi} = -1 (Two-parameter
Uniform).
