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Math Help - Confidence Interval

  1. #1
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    Confidence Interval

    Construct a symmetric two-sided (1-\alpha)100\% confidence interval for the unknown parameter \beta > 0 in a Beta(1,\beta) sample.

    The hint is to find the MLE of \beta and determine the distribution of -log(1-X) for a Beta(1,\beta) random variable X
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  2. #2
    MHF Contributor matheagle's Avatar
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    Write your likelihood function, take the logarithm and then differentiate to find the MLE of beta.
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  3. #3
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    I'm trying to write out the loglikelihood function for Beta(1,\beta)

    I simply don't understand the pdf of the beta distribution. Its pdf is \frac{x^{\alpha-1}(1-x)^{\beta-1}}{B(\alpha,\beta)} In my case, it would be \frac{(1-x)^{\beta-1}}{B(1,\beta)}

    It's using the definition to define itself, how does this make any sense?
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  4. #4
    MHF Contributor matheagle's Avatar
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    use  x_i and take the product from 1 to n
    and write the constants with respect to the gamma function.
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