Doubt with random numbers in parametric Bootstrap

[haplo]

Hello all,

Suppose I have a set of datas 8...20, with mean 10 and lambda 1/10=0.1 . I want to make a parametric bootstrap, supousing my datas come from an exponential distribution.

So now I may construct my random samples from an exponential distribution with lambda=0.1 . My problem is I do not know from where those random number come.

Do I have to construct my resamples from random numbers between the smallest and greatest values from my set of datas (8,20)? If not so, From random numbers between 0-1?

Any kind of help will be appreciated. Thanks in advance

 

[katxt]

a set of data 8...20, with mean 10 and lambda 1/10=0.1

Is this the actual data? If so, it seems unlikely that it is exponential because of the lack of small values (about half of the data would be below about 7) so I would resample the data.

 

[haplo]

Is this the actual data?

Thanks katxt for your answer. It is only an example. The main question is abut the random numbers. It is not important if is a normal, exponential, lognormal...

My assumption is that I must resample from random numbers between the smallest and greatest set of datas, but I am not absolutely sure about this

 

[katxt]

It depends on what you want to do.
There some distinction between resampling and simulation. Resampling automatically produces numbers within the same range and so is of limited help if your interest is in the tails - predicting 100 year floods for example. It's good for giving information about the accuracy of the mean or variance. Simulation using a generating formula will produce the required tails occasionally but this is really a false promise because you need to find the parameters for the formula. Your estimates won't be perfect and the model is only an approximation to the real world anyway.
If you are doing a risk analysis simulation, the there are practical advantages in using the fitted formula if the model is appropriate.

 

[haplo]

Thank you very much katxt. In the scenario I work the best is the resampling, so as for your answer, the best is to use the datas in the range, as I thought.

I am trully newbie in bootstraping, and your answer is just what I needed. Thank you again