Thread: How similar is the sampled distribution to the population?

Hi,
I wrote a similar question over here but received no replies. Since then I have refined my question and hopefully I can now express it more clearly and in the correct place.

I am sampling values from a Weibull Distribution (a heavy tail distribution). I want to know how many sampled values are needed for the sample distribution to be within X% of the population distribution?

For example I have been sampling 100, 200, 300, etc values from my distribution and from a visual inspection of the sample and population CDFs I can see that the more samples I have the closer the sample CDF gets to the population CDF. Obviously they will perfectly match once the entire population has been sampled. What I wanted is a way to quantify numerically how similar these sample distributions are to the population.

I understand conference intervals allow me to work out a similar metric for the sample mean compared to the population mean. I have also been reading various articles online to try and find an answer, but I have yet to find anything applicable.

I would be grateful for anyone to show me how to work this out for a Weibull Distribution. Failing that just showing me with a Normal Distribution would be great. If I can’t quantify the value with an equation, I will resort to running Monte Carlo style simulations to pick random samples from the population and compare the sample and population CDFs with an R-Square test, or a Kolmogorov Smirnov test.

Thanks for any help

Originally Posted by bramp

Hi,
I wrote a similar question over here but received no replies. Since then I have refined my question and hopefully I can now express it more clearly and in the correct place.

I am sampling values from a Weibull Distribution (a heavy tail distribution). I want to know how many sampled values are needed for the sample distribution to be within X% of the population distribution?

For example I have been sampling 100, 200, 300, etc values from my distribution and from a visual inspection of the sample and population CDFs I can see that the more samples I have the closer the sample CDF gets to the population CDF. Obviously they will perfectly match once the entire population has been sampled. What I wanted is a way to quantify numerically how similar these sample distributions are to the population.

I understand conference intervals allow me to work out a similar metric for the sample mean compared to the population mean. I have also been reading various articles online to try and find an answer, but I have yet to find anything applicable.

I would be grateful for anyone to show me how to work this out for a Weibull Distribution. Failing that just showing me with a Normal Distribution would be great. If I can’t quantify the value with an equation, I will resort to running Monte Carlo style simulations to pick random samples from the population and compare the sample and population CDFs with an R-Square test, or a Kolmogorov Smirnov test.

Thanks for any help

Are you estimating the parameters of the Weibull from your data? If not look at the KS statistic, how large a sample will you need for the KS critical value (lets say the 95% value) to be as small as you would like.

Alternativly think look at the posssibility of a boot strap-like method.

RonL