given a arbitrary distribution, can we find out its confidence interval?

[W_Heisenberg]

given a arbitrary distribution, can we find out its confidence interval?

say alpha = 0.95?

 

[beeflobill]

Hopefully I'm not patronizing in my interpretation of the question, but I believe I can answer this. The answer is no. This is because a confidence interval is a function of a particular sample from a population. So, different samples taken from the same population can have different confidence intervals.

However, given a description of a distribution, I believe it is possible to find equations which would determine the confidence interval corresponding to a sample from a population assumed to have the said distribution.

In other words:

Distribution  ===> Confidence interval

doesn't have enough information.

But:

   Assumed Distribution  ===> Hard math work
      /\                         ||
      ||                         \/
Population ===> Sample  ===> Equations  ===> Confidence interval

I think describes my understanding of what has to happen to get a confidence interval. Perhaps there is a little too much magic in the "Hard math work" step, but I think this answers the question-as-asked. If anyone statistics guru disagrees, they can blast me into space but, I'd prefer a more gentle correction .

 

[W_Heisenberg]

yes, I finally figure this out.

You are right.

Hopefully I'm not patronizing in my interpretation of the question, but I believe I can answer this. The answer is no. This is because a confidence interval is a function of a particular sample from a population. So, different samples taken from the same population can have different confidence intervals.

However, given a description of a distribution, I believe it is possible to find equations which would determine the confidence interval corresponding to a sample from a population assumed to have the said distribution.

In other words:

Distribution  ===> Confidence interval

doesn't have enough information.

But:

   Assumed Distribution  ===> Hard math work
      /\                         ||
      ||                         \/
Population ===> Sample  ===> Equations  ===> Confidence interval

I think describes my understanding of what has to happen to get a confidence interval. Perhaps there is a little too much magic in the "Hard math work" step, but I think this answers the question-as-asked. If anyone statistics guru disagrees, they can blast me into space but, I'd prefer a more gentle correction .