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What are examples of probability density functions $f(x|\theta)$ on $[0,1] \times [0,1]$ that are $C^2$ and satisfy the monotone likelihood ratio conditions?

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Did you consider accepting answers to some related previous posts of yours? Such as math.stackexchange.com/q/36942/6179 or math.stackexchange.com/q/29988/6179 or math.stackexchange.com/q/29855/6179. Or following the specific suggestions made in some of these about the MLR property? –  Did Jun 1 '11 at 6:18
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