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I have a model where time is the response variable. I'd like to generate confidence intervals for the estimates. I have established that the error in the estimation is roughly normally distributed (it may be more cauchy). The Mean and Median are very different, with the median more accurately representing the middle of the data. Am I allowed to use the median for my confidence interface and if so is there a different method for doing so?

I have reviewed this question: Confidence interval for median but it is not clear if they are trying to accomplish the same thing I am.

EDIT The model is for an estimation of the amount of time a process takes to complete. I performed a linear regression and established that the model has a relatively good fit. I then took repeatedly (2000 times) took a random sample of 75% of the original sample and rebuilt the model. I then predicted the time for the remaining 25%, and stored the error in each case. This led to ~90000 results, which roughly follow a normal distribution (or possibly cauchy) I would like to find an estimate for the confidence interval of an individual result, e.g. for one specific process the actual time taken was 46 seconds, and the predicted time taken was 1 minute. I'd like to be able to say with 95% certainty that my estimate is accurate within +- 15 seconds (for example).

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    $\begingroup$ The confidence interval of an estimate is not directly related to mean or median. Your question doesn't give enough information to give solid advice. $\endgroup$
    – Roland
    Commented Jun 18, 2014 at 14:55
  • $\begingroup$ For this question to be answerable, we need to know more about what is being estimated, how it is being estimated, and the statistical assumptions underlying those estimates. For instance, you might be interested in the coefficient of variation of a population presumed to follow some Gamma distribution or perhaps you would like to have confidence intervals for the upper quartile of a population with a Poisson distribution: the answers to those questions--both of which can be seen as instances of your situation--would be rather different. $\endgroup$
    – whuber ♦
    Commented Jun 18, 2014 at 15:13

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