MATLAB: How to get AIC, confidence intervals, and distribution parameters for fitting functions

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How can I get AIC, Confidence Intervals, and Parameters for fitting functions? In particular, I need to use the following functions for distribution fitting with censoring, but I don’t know if these functions can return AIC, confidence intervals, and distribution parameter estimates at set confidence intervals.
  • "evfit" for extreme value parameter estimates
  • "expfit" for exponential parameter estimates
  • "gamfit" for gamma parameter estimates
  • "lognfit" for lognormal parameter estimates
  • "normfit" for normal parameter estimates
  • "wblfit" for Weibull parameter estimates

Best Answer

There are specific functions for obtaining AIC, confidence intervals, and distribution parameter estimates related to each fitting functions respectively. Details are provided below:
1) The fitting functions ("evfit", "expfit", "gamfit", "lognfit", "normfit", "wblfit") contain an option to specify confidence intervals. Estimates under certain confidence intervals will be returned.
2) The likelihood functions ("evlike", "explike", "gamlike", "lognlike", "normlike", "wbllike") returns the negative log-likelihood given estimates from the previous step as input.
3) The "aicbic" function returns Akaike information criteria (AIC) given log-likelihood and number of estimated parameters.
Taking the Extreme value parameter estimates as an example...
1) "parmhat = evfit(data)" returns the estimates for 95% confidence intervals by default. It can also return estimates for defined confidence interval from the "alpha" value via the command "[parmhat,parmci] = evfit(data,alpha)".
https://www.mathworks.com/help/stats/evfit.html#brx09qo-646
2) "nlogL = evlike(params,data)" returns the negative of the log-likelihood for the extreme value distribution.
https://www.mathworks.com/help/stats/evlike.html
3) "aicbic(logL, numParam)" returns AIC given the log-likelihood and number of estimated parameters from previous two steps.
https://www.mathworks.com/help/econ/aicbic.html#br76hp9-1-numParam
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