How can I get the bootstrapped CI for range statistics?

Hi,

I am trying to find the bootstrap confidence interval of the range value for cummulative normal random numbers.

How can I use bootci to find the correct CI of the range.

I wrote the test code below but It returns the wrong CI;

z=randn(100,1)
mn=mean(z)
sd=std(z)

range=fndrng(z)

f=@(z) fndrng(z)

[cirange, bootstatrange]=bootci(500,{f, z});
cirange
histogram(bootstatrange)

function  rng=fndrng(x)
cums=0;
for i=1:length(x)
   y(i)=cums+x(i)- mean(x);
    cums=y(i);
end
rng=max(y)-min(y);
end

[Jeff Miller]

Could you explain a bit more about what you are trying to do? It is not really clear what you mean by "cumulative" normal random numbers, because "cumulative" commonly refers to a type of tabulation of random numbers rather than to the random numbers themselves. (For that reason, it is hard to understand the purpose of your cumulative calculation within fndrng.) Also, it might help if you say how you know this code is not giving you the correct answer?

[Okan Fistikoglu]

Thank you for your interest, I generate a column vector x(i) with 100 normally distributed random numbers then calculate the accumulated vector y(i) like cusum (cumulative sum) as y(i)=y(i-1)+ x(i)-mean(x) and I find the range of y which is difference max(y) and min(y). Then finally I get the CI of range parameter of y by bootstrapping. The problem is the CI of the range (calculating by bootci and its default settings) seems problematic considering the histogram of the bootstraped range values.

[Jeff Miller]

"I generate a column...range parameter of y by bootstrapping". Yes, that is a very clear description of what your code does (though I still don't see why you want to do this). Well, no matter.

"seems problematic" how? Running your code, I see that the histogram of range values is skewed with a long tail at the high end. Maybe the CI seems problematic to you because it approaches the bottom of the histogram much more closely than it approaches the top? If that is what you are unhappy about, maybe one of the other methods of computing the bootstrap ci will look better. For example, you can use

[cirange, bootstatrange]=bootci(5000,{f, z}, 'type','per');  % or type 'cper'--see docs

to request a ci computed simply based on the percentiles of the bootstrap distribution, just the same as

bpcts = prctile(bootstatrange,[2.5, 97.5])