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I have a sample of data that follows a certain distribution with known parameters. How can I estimate the confidence interval based on this sample, without using the quantile function?

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    $\begingroup$ Confidence interval ... for what quantity? $\endgroup$ – Glen_b Jan 26 '14 at 23:54
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If you are certain of the population distribution and its parameters, you are done. Why would you want to compute a confidence interval to quantify the uncertainty of an estimate from a sample, when you already know exactly the distribution of the population?

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