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I am trying to find a prior distribution for a proportion $\theta$ that is highly informative i.e. it is almost point mass at $\theta$ but I am not able to find such distribution that is valid for a proportion. I could use easily a normal distribution with really small variance but our professor said that it would be incorrect because the support is the whole $\mathbb{R}$ and $\theta\in [0,1]$.Thus, I restricted my self to beta distributions but I cannot find a point mass beta distribution.

So I would like some help in order to find such distribution even if it's not a beta distribution.

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    $\begingroup$ What's wrong with the beta distribution? You can make it as concentrated as you want around a single value, e.g., a Beta(1000,1000) has a mean of 0.5 and a standard deviation of 0.011. $\endgroup$
    – jbowman
    Apr 4, 2019 at 17:38
  • $\begingroup$ @jbowman you are completely right!Thank you. $\endgroup$
    – G1I2A
    Apr 4, 2019 at 17:48
  • $\begingroup$ You can also use truncated normal distribution. $\endgroup$
    – Tim
    Apr 4, 2019 at 19:15

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As already noted in comments, you can use beta distribution with high values of parameters. If that's easier, you can re-parametrize beta distribution in terms of location and scale. But you can also use normal distribution, Laplace distribution, or whatever distribution you want but with truncating it into $(0, 1)$ interval.

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