# How to get a weighted-estimate for mean difference?

I wanted to estimate the difference of two means (say: $\mu_1$ and $\mu_2$). I have the estimate of means (say: $m_1$ and $m_2$) with variance estimates (say: $v_1$ and $v_2$).

How do I calculate the weighted-estimate for difference of means ($\mu_2$ - $\mu_1$)?

I am thinking these two should work (in the order of preference):

1. $\frac{v_1}{v_2} m_2 - m_1$
2. $\frac {v_1} {v_2 + v_1} m_2 - \frac {v_2} {v_2 + v_1} m_1$

This problem may seem like the Behrens-Fisher problem. However, in my case the data is NOT normally distributed.

Any help is appreciated.

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Is it for hypothesis testing? May be you could consider non-parametric statistics like Mann-Witney U or any other that are not dependent on the distribution assumptions. There are also weighted analogs of statistics for them. –  Dmitrij Celov Jul 4 '11 at 11:30
@Dmitrij No this is just an estimate that I am interested in. No hypothesis testing like scenario. –  suncoolsu Jul 4 '11 at 11:32
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