UMP test for hypergeometric distribution $P(X=x|N,D,n)=\frac{^DC_x \times ^{(N-D)}C_{(n-x)}}{^NC_n}$
Now, I was trying to test for $H_0:D\le D_0$ vs $H_1:D>D_0$ using likelihood ratio test.
But to find the maximum likelihood estimate of $D,$ the terms are in $^DC_x$ form, so I could not proceed further.
Can anyone provide me how to find the estimate of $D$ or provide some other test for this problem?

Here $X\sim \operatorname{HyperGeo}(N,D,n) . $
We need to find (if it exists) the UMP test of $\mathcal H_0: D\leq D_0$ vs $\mathcal H_1: D> D_0.$
What should be the approach to tackle such problem, in general?
Possible line of approach:
$\bullet$ Check whether the family of distributions possesses the property of Monotone Likelihood Ratio (MLR) through any statistic $T(\mathbf x). $
$\bullet$ If so, hypotheses like above can be assessed via theorem of Karlin-Rubin which does show the existence of a UMP level $\alpha$ test.

Edit: How to calculate the MLE of $D: ~\hat D?$ One needs to solve
$ \mathcal L( D|\mathbf x) \geq \mathcal L( D-1|\mathbf x) .$ From this, one would get a bound on $D.$ Can this be MLE of $D?$
