formula under CPQD as follows: Similarly, the distributional parameters are bounded under NSM and MTR. The specific forms of sharp bounds on marginal distributions of Y$_{0}$ and Y$_{1}$, their joint distribution, and the DTE under M. 1 − M. 4 , NSM, and MTR are provided in Theorem 2 in Appendix. Lastly, marginal distribution bounds under NSM, CPQD, and MTR and marginal distribution bounds under CPQD and MTR are identical to those under NSM and MTR and those under MTR, respectively, since CPQD does not affect bounds on marginal distributions. However, it is not straightforward to construct sharp bounds on the joint distribution and the DTE under these three conditions or under CPQD and MTR, as both CPQD and MTR directly restrict the joint distribution as different types of conditions. To the best of my knowledge, there exist no results on the sharp bounds on the joint distribution and DTE when support restrictions such as MTR are combined with various dependence restriction such as quadrant dependence. This is beyond the scope of this paper. This section presents numerical examples to illustrate how bounds on distributional parameters are tightened by the restrictions considered in this paper. The potential outcomes and selection equations are given as follows: where ( U, ε ) ∼ i.i.d.N (0 , I$_{2}$ ), η ∼ χ $^{2}$( k ), and η ⊥ ( U, ε ) for a positive integer k. 25 Y$_{0}$ = ρU + ε, Y$_{1}$ = Y$_{0}$ + η, D ( Z ) = 1 ( Z ≥ U ) , 5 Numerical Examples F $^{L}$( y$_{0}$, y$_{1}$ ) = sup z ∈Z $^{{}$P ( y$_{0}$ | 0 , z ) L sm 10 ( y$_{1}$, z ) + L wst 01 ( y$_{0}$, z ) P ( y$_{1}$ | 1 , z ) $^{}}$, F U ( y$_{0}$, y$_{1}$ ) = inf z ∈Z    min $^{{}$P ( y$_{0}$ | 0 , z ) (1 − p ( z )) , U wst 10 ( y, z ) } + min { U sm 01 ( y$_{0}$, z ) , P ( y$_{1}$ | 1 , z ) p ( z ) }   $_{}$.