how to get the MLE

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I need some one help me. My question is ,
Given Xi (i=1,....n) is normal distribution with mean u1 and sd 1
Yi (i=1,....n) is normal distribution with mean u2 and sd 1
also given constraint u1 is smaller than u2

what's the Maximum likelihood estimate for u1 and u2

I know how to get the MLE without the constraint.
Please help me. Thank you

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关键词：Get How MLE The distribution question without normal Thank

再问一声有没有人知道？是不是很难解？

貌似是要求

Maximum Likelihood estimation for a mixture of Gaussians

For a mixture of different normal distributions (a Gaussian Mixture Model),
the correct parameters for mean and standard deviation for each Gaussian
cannot be computed by simply taking mean and std of the entire data set.
The observed data must be divided into several Gaussians,
each of with its own mean and standard deviation.
One approach for obtaining the paramaters for each Gaussian is to
apply the algorithm for Expectation Maximization.

  http://www.mathworks.com/help/toolbox/stats/gmdistribution.fit.html

谢谢答复。
不是mixture of univariate normal distribution. 所有的Xi 和Yi are indepentent. 如没有constraint ( u1 is smaller than u2)的话， MLE for Xi and Yi are u1 and u2. With the constraint, I really don't know to solve it.

假设

    X:mu1=3;sd1=7

      数据在matlab模拟产生

    Y:mu2=9;sd2=2

      数据在matlab模拟产生.

请问你要求甚么?

  

我查了这应是保序回归（isotonic regression）。我需要的是如何推导出u1和u2的极大似然估计。多谢。

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