What I am trying to do is to fit a log-normal distribution to a data-set, and then determine confidence and prediction intervals for the fitted distribution - not just for the mean and sd estimates.
My final goal is to be able to say that if we repeated a set of measurements, then 95 % of the values would fall below some specific value. I can obviously do that from the fitted distribution itself (or rather the cumulative version), but I'm thinking that will under-estimate the probability because I need to include the variability in the estimates and/or fit itself first?
If I use the following code:
require(MASS) set.seed(123) x<-rlnorm(100) fit<-fitdistr(x,"lognormal")
then R will calculate a log-normal distribution fitted to my data. The fitdistr function will return the estimated mean and sd (along with standard errors for these estimates).
meanlog sdlog 0.09040591 0.90824033 (0.09082403) (0.06422229)
I understand that these will then allow me to plot the fitted distribution (and histogram) using ggplot2 with the following code:
meanlog<-fit$estimate[] sdlog<-fit$estimate[] binwidth<-abs(max(x)-min(x))/20 qplot(x,geom="blank")+geom_histogram(binwidth=binwidth,aes(y= ..density..))+stat_function(fun=dlnorm,arg=list(meanlog=meanlog,sdlog=sdlog),colour="red")
However, what I really want to do is to plot the confidence interval and/or prediction interval of this fitted distribution. Something similar to how ggplot2 does with stat_smooth, something like:
x<-seq(1,100) y<-x+rnorm(x,sd=10) qplot(x,y,geom="point")+stat_smooth(method='lm',se=T)
I can use confint(fit) to extract the confidence intervals for the estimated mean and sd, but I think I misunderstand the maths because I can't for the life of me work out how to use those in order to be able to calculate the confidence interval for the actual distribution. So neither can I work out the prediction interval. I've tried writing my own function for the log-normal distribution to input various combinations of the confidence intervals from confint manually - but that doesn't work. Obviously a confidence interval of the estimate does not directly give you the confidence interval of the line. And, therefore, neither the prediction interval.
I would really appreciate anyone who can walk me through this please!